For the given set of reactions the base present in each reaction should be identified that if it is sufficient to deprotonate the terminal alkyne . Concept Introduction : Acid-Base Reaction: This type of chemical process typified by the exchange of one or more hydrogens ions H + , between species that may be neutral molecules or electrically charged ions. Chemical equilibrium : The term applied to reversible chemical reactions. It is the point at which the rate of the forward reaction is equal to the rate of the reverse reaction. The equilibrium is achieved; the concentrations of reactant and products become constant.

Question

Want to see the full answer?

Answer 1

Question

Chapter 10.3, Problem 5PTS

(a)

Interpretation Introduction

Interpretation:

For the given set of reactions the base present in each reaction should be identified that if it is sufficient to deprotonate the terminal alkyne.

Concept Introduction:

Acid-Base Reaction: This type of chemical process typified by the exchange of one or more hydrogens ions H⁺, between species that may be neutral molecules or electrically charged ions.

Chemical equilibrium: The term applied to reversible chemical reactions. It is the point at which the rate of the forward reaction is equal to the rate of the reverse reaction. The equilibrium is achieved; the concentrations of reactant and products become constant.

(b)

Interpretation Introduction

Interpretation:

For the given set of reactions the base present in each reaction should be identified that if it is sufficient to deprotonate the terminal alkyne.

Concept Introduction:

Acid-Base Reaction: This type of chemical process typified by the exchange of one or more hydrogens ions H⁺, between species that may be neutral molecules or electrically charged ions.

Chemical equilibrium: The term applied to reversible chemical reactions. It is the point at which the rate of the forward reaction is equal to the rate of the reverse reaction. The equilibrium is achieved; the concentrations of reactant and products become constant.

(c)

Interpretation Introduction

Interpretation:

For the given set of reactions the base present in each reaction should be identified that if it is sufficient to deprotonate the terminal alkyne.

Concept Introduction:

Acid-Base Reaction: This type of chemical process typified by the exchange of one or more hydrogens ions H⁺, between species that may be neutral molecules or electrically charged ions.

Chemical equilibrium: The term applied to reversible chemical reactions. It is the point at which the rate of the forward reaction is equal to the rate of the reverse reaction. The equilibrium is achieved; the concentrations of reactant and products become constant.

(d)

Interpretation Introduction

Interpretation:

For the given set of reactions the base present in each reaction should be identified that if it is sufficient to deprotonate the terminal alkyne.

Concept Introduction:

Acid-Base Reaction: This type of chemical process typified by the exchange of one or more hydrogens ions H⁺, between species that may be neutral molecules or electrically charged ions.

Chemical equilibrium: The term applied to reversible chemical reactions. It is the point at which the rate of the forward reaction is equal to the rate of the reverse reaction. The equilibrium is achieved; the concentrations of reactant and products become constant.

(e).

Interpretation Introduction

Interpretation:

For the given set of reactions the base present in each reaction should be identified that if it is sufficient to deprotonate the terminal alkyne.

Concept Introduction:

Acid-Base Reaction: This type of chemical process typified by the exchange of one or more hydrogens ions H⁺, between species that may be neutral molecules or electrically charged ions.

Chemical equilibrium: The term applied to reversible chemical reactions. It is the point at which the rate of the forward reaction is equal to the rate of the reverse reaction. The equilibrium is achieved; the concentrations of reactant and products become constant.

(f).

Interpretation Introduction

Interpretation:

For the given set of reactions the base present in each reaction should be identified that if it is sufficient to deprotonate the terminal alkyne.

Concept Introduction:

Acid-Base Reaction: This type of chemical process typified by the exchange of one or more hydrogens ions H⁺, between species that may be neutral molecules or electrically charged ions.

Chemical equilibrium: The term applied to reversible chemical reactions. It is the point at which the rate of the forward reaction is equal to the rate of the reverse reaction. The equilibrium is achieved; the concentrations of reactant and products become constant.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Students have asked these similar questions

Indicate whether the following two statements are correct or not:- The S8 heterocycle is the origin of a family of compounds- Most of the elements that give rise to stable heterocycles belong to group d.

could someone draw curly arrow mechanism for this question please

In the phase diagram of quartz (SiO2), indicate what happens as the pressure increases.

Answer 2

Question

Chapter 10.3, Problem 5PTS

(a)

Interpretation Introduction

Interpretation:

For the given set of reactions the base present in each reaction should be identified that if it is sufficient to deprotonate the terminal alkyne.

Concept Introduction:

Acid-Base Reaction: This type of chemical process typified by the exchange of one or more hydrogens ions H⁺, between species that may be neutral molecules or electrically charged ions.

Chemical equilibrium: The term applied to reversible chemical reactions. It is the point at which the rate of the forward reaction is equal to the rate of the reverse reaction. The equilibrium is achieved; the concentrations of reactant and products become constant.

(b)

Interpretation Introduction

Interpretation:

For the given set of reactions the base present in each reaction should be identified that if it is sufficient to deprotonate the terminal alkyne.

Concept Introduction:

Acid-Base Reaction: This type of chemical process typified by the exchange of one or more hydrogens ions H⁺, between species that may be neutral molecules or electrically charged ions.

Chemical equilibrium: The term applied to reversible chemical reactions. It is the point at which the rate of the forward reaction is equal to the rate of the reverse reaction. The equilibrium is achieved; the concentrations of reactant and products become constant.

(c)

Interpretation Introduction

Interpretation:

For the given set of reactions the base present in each reaction should be identified that if it is sufficient to deprotonate the terminal alkyne.

Concept Introduction:

Acid-Base Reaction: This type of chemical process typified by the exchange of one or more hydrogens ions H⁺, between species that may be neutral molecules or electrically charged ions.

Chemical equilibrium: The term applied to reversible chemical reactions. It is the point at which the rate of the forward reaction is equal to the rate of the reverse reaction. The equilibrium is achieved; the concentrations of reactant and products become constant.

(d)

Interpretation Introduction

Interpretation:

For the given set of reactions the base present in each reaction should be identified that if it is sufficient to deprotonate the terminal alkyne.

Concept Introduction:

Acid-Base Reaction: This type of chemical process typified by the exchange of one or more hydrogens ions H⁺, between species that may be neutral molecules or electrically charged ions.

Chemical equilibrium: The term applied to reversible chemical reactions. It is the point at which the rate of the forward reaction is equal to the rate of the reverse reaction. The equilibrium is achieved; the concentrations of reactant and products become constant.

(e).

Interpretation Introduction

Interpretation:

For the given set of reactions the base present in each reaction should be identified that if it is sufficient to deprotonate the terminal alkyne.

Concept Introduction:

Acid-Base Reaction: This type of chemical process typified by the exchange of one or more hydrogens ions H⁺, between species that may be neutral molecules or electrically charged ions.

Chemical equilibrium: The term applied to reversible chemical reactions. It is the point at which the rate of the forward reaction is equal to the rate of the reverse reaction. The equilibrium is achieved; the concentrations of reactant and products become constant.

(f).

Interpretation Introduction

Interpretation:

For the given set of reactions the base present in each reaction should be identified that if it is sufficient to deprotonate the terminal alkyne.

Concept Introduction:

Acid-Base Reaction: This type of chemical process typified by the exchange of one or more hydrogens ions H⁺, between species that may be neutral molecules or electrically charged ions.

Chemical equilibrium: The term applied to reversible chemical reactions. It is the point at which the rate of the forward reaction is equal to the rate of the reverse reaction. The equilibrium is achieved; the concentrations of reactant and products become constant.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 10.3, Problem 5PTS

(a)

Interpretation Introduction

Interpretation:

For the given set of reactions the base present in each reaction should be identified that if it is sufficient to deprotonate the terminal alkyne.

Concept Introduction:

Acid-Base Reaction: This type of chemical process typified by the exchange of one or more hydrogens ions H⁺, between species that may be neutral molecules or electrically charged ions.

Chemical equilibrium: The term applied to reversible chemical reactions. It is the point at which the rate of the forward reaction is equal to the rate of the reverse reaction. The equilibrium is achieved; the concentrations of reactant and products become constant.

(b)

Interpretation Introduction

Interpretation:

For the given set of reactions the base present in each reaction should be identified that if it is sufficient to deprotonate the terminal alkyne.

Concept Introduction:

Acid-Base Reaction: This type of chemical process typified by the exchange of one or more hydrogens ions H⁺, between species that may be neutral molecules or electrically charged ions.

Chemical equilibrium: The term applied to reversible chemical reactions. It is the point at which the rate of the forward reaction is equal to the rate of the reverse reaction. The equilibrium is achieved; the concentrations of reactant and products become constant.

(c)

Interpretation Introduction

Interpretation:

For the given set of reactions the base present in each reaction should be identified that if it is sufficient to deprotonate the terminal alkyne.

Concept Introduction:

Acid-Base Reaction: This type of chemical process typified by the exchange of one or more hydrogens ions H⁺, between species that may be neutral molecules or electrically charged ions.

Chemical equilibrium: The term applied to reversible chemical reactions. It is the point at which the rate of the forward reaction is equal to the rate of the reverse reaction. The equilibrium is achieved; the concentrations of reactant and products become constant.

(d)

Interpretation Introduction

Interpretation:

For the given set of reactions the base present in each reaction should be identified that if it is sufficient to deprotonate the terminal alkyne.

Concept Introduction:

Acid-Base Reaction: This type of chemical process typified by the exchange of one or more hydrogens ions H⁺, between species that may be neutral molecules or electrically charged ions.

Chemical equilibrium: The term applied to reversible chemical reactions. It is the point at which the rate of the forward reaction is equal to the rate of the reverse reaction. The equilibrium is achieved; the concentrations of reactant and products become constant.

(e).

Interpretation Introduction

Interpretation:

For the given set of reactions the base present in each reaction should be identified that if it is sufficient to deprotonate the terminal alkyne.

Concept Introduction:

Acid-Base Reaction: This type of chemical process typified by the exchange of one or more hydrogens ions H⁺, between species that may be neutral molecules or electrically charged ions.

Chemical equilibrium: The term applied to reversible chemical reactions. It is the point at which the rate of the forward reaction is equal to the rate of the reverse reaction. The equilibrium is achieved; the concentrations of reactant and products become constant.

(f).

Interpretation Introduction

Interpretation:

For the given set of reactions the base present in each reaction should be identified that if it is sufficient to deprotonate the terminal alkyne.

Concept Introduction:

Acid-Base Reaction: This type of chemical process typified by the exchange of one or more hydrogens ions H⁺, between species that may be neutral molecules or electrically charged ions.

Chemical equilibrium: The term applied to reversible chemical reactions. It is the point at which the rate of the forward reaction is equal to the rate of the reverse reaction. The equilibrium is achieved; the concentrations of reactant and products become constant.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 10.3, Problem 5PTS

(a)

Interpretation Introduction

Interpretation:

For the given set of reactions the base present in each reaction should be identified that if it is sufficient to deprotonate the terminal alkyne.

Concept Introduction:

Acid-Base Reaction: This type of chemical process typified by the exchange of one or more hydrogens ions H⁺, between species that may be neutral molecules or electrically charged ions.

Chemical equilibrium: The term applied to reversible chemical reactions. It is the point at which the rate of the forward reaction is equal to the rate of the reverse reaction. The equilibrium is achieved; the concentrations of reactant and products become constant.

(b)

Interpretation Introduction

Interpretation:

For the given set of reactions the base present in each reaction should be identified that if it is sufficient to deprotonate the terminal alkyne.

Concept Introduction:

Acid-Base Reaction: This type of chemical process typified by the exchange of one or more hydrogens ions H⁺, between species that may be neutral molecules or electrically charged ions.

Chemical equilibrium: The term applied to reversible chemical reactions. It is the point at which the rate of the forward reaction is equal to the rate of the reverse reaction. The equilibrium is achieved; the concentrations of reactant and products become constant.

(c)

Interpretation Introduction

Interpretation:

For the given set of reactions the base present in each reaction should be identified that if it is sufficient to deprotonate the terminal alkyne.

Concept Introduction:

Acid-Base Reaction: This type of chemical process typified by the exchange of one or more hydrogens ions H⁺, between species that may be neutral molecules or electrically charged ions.

Chemical equilibrium: The term applied to reversible chemical reactions. It is the point at which the rate of the forward reaction is equal to the rate of the reverse reaction. The equilibrium is achieved; the concentrations of reactant and products become constant.

(d)

Interpretation Introduction

Interpretation:

For the given set of reactions the base present in each reaction should be identified that if it is sufficient to deprotonate the terminal alkyne.

Concept Introduction:

Acid-Base Reaction: This type of chemical process typified by the exchange of one or more hydrogens ions H⁺, between species that may be neutral molecules or electrically charged ions.

Chemical equilibrium: The term applied to reversible chemical reactions. It is the point at which the rate of the forward reaction is equal to the rate of the reverse reaction. The equilibrium is achieved; the concentrations of reactant and products become constant.

(e).

Interpretation Introduction

Interpretation:

For the given set of reactions the base present in each reaction should be identified that if it is sufficient to deprotonate the terminal alkyne.

Concept Introduction:

Acid-Base Reaction: This type of chemical process typified by the exchange of one or more hydrogens ions H⁺, between species that may be neutral molecules or electrically charged ions.

Chemical equilibrium: The term applied to reversible chemical reactions. It is the point at which the rate of the forward reaction is equal to the rate of the reverse reaction. The equilibrium is achieved; the concentrations of reactant and products become constant.

(f).

Interpretation Introduction

Interpretation:

For the given set of reactions the base present in each reaction should be identified that if it is sufficient to deprotonate the terminal alkyne.

Concept Introduction:

Acid-Base Reaction: This type of chemical process typified by the exchange of one or more hydrogens ions H⁺, between species that may be neutral molecules or electrically charged ions.

Chemical equilibrium: The term applied to reversible chemical reactions. It is the point at which the rate of the forward reaction is equal to the rate of the reverse reaction. The equilibrium is achieved; the concentrations of reactant and products become constant.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 5

Chapter 10.3, Problem 5PTS

(a)

Interpretation Introduction

Interpretation:

For the given set of reactions the base present in each reaction should be identified that if it is sufficient to deprotonate the terminal alkyne.

Concept Introduction:

Acid-Base Reaction: This type of chemical process typified by the exchange of one or more hydrogens ions H⁺, between species that may be neutral molecules or electrically charged ions.

Chemical equilibrium: The term applied to reversible chemical reactions. It is the point at which the rate of the forward reaction is equal to the rate of the reverse reaction. The equilibrium is achieved; the concentrations of reactant and products become constant.

(b)

Interpretation Introduction

Interpretation:

For the given set of reactions the base present in each reaction should be identified that if it is sufficient to deprotonate the terminal alkyne.

Concept Introduction:

Acid-Base Reaction: This type of chemical process typified by the exchange of one or more hydrogens ions H⁺, between species that may be neutral molecules or electrically charged ions.

Chemical equilibrium: The term applied to reversible chemical reactions. It is the point at which the rate of the forward reaction is equal to the rate of the reverse reaction. The equilibrium is achieved; the concentrations of reactant and products become constant.

(c)

Interpretation Introduction

Interpretation:

For the given set of reactions the base present in each reaction should be identified that if it is sufficient to deprotonate the terminal alkyne.

Concept Introduction:

Acid-Base Reaction: This type of chemical process typified by the exchange of one or more hydrogens ions H⁺, between species that may be neutral molecules or electrically charged ions.

Chemical equilibrium: The term applied to reversible chemical reactions. It is the point at which the rate of the forward reaction is equal to the rate of the reverse reaction. The equilibrium is achieved; the concentrations of reactant and products become constant.

(d)

Interpretation Introduction

Interpretation:

For the given set of reactions the base present in each reaction should be identified that if it is sufficient to deprotonate the terminal alkyne.

Concept Introduction:

Acid-Base Reaction: This type of chemical process typified by the exchange of one or more hydrogens ions H⁺, between species that may be neutral molecules or electrically charged ions.

Chemical equilibrium: The term applied to reversible chemical reactions. It is the point at which the rate of the forward reaction is equal to the rate of the reverse reaction. The equilibrium is achieved; the concentrations of reactant and products become constant.

(e).

Interpretation Introduction

Interpretation:

For the given set of reactions the base present in each reaction should be identified that if it is sufficient to deprotonate the terminal alkyne.

Concept Introduction:

Acid-Base Reaction: This type of chemical process typified by the exchange of one or more hydrogens ions H⁺, between species that may be neutral molecules or electrically charged ions.

Chemical equilibrium: The term applied to reversible chemical reactions. It is the point at which the rate of the forward reaction is equal to the rate of the reverse reaction. The equilibrium is achieved; the concentrations of reactant and products become constant.

(f).

Interpretation Introduction

Interpretation:

For the given set of reactions the base present in each reaction should be identified that if it is sufficient to deprotonate the terminal alkyne.

Concept Introduction:

Acid-Base Reaction: This type of chemical process typified by the exchange of one or more hydrogens ions H⁺, between species that may be neutral molecules or electrically charged ions.

Chemical equilibrium: The term applied to reversible chemical reactions. It is the point at which the rate of the forward reaction is equal to the rate of the reverse reaction. The equilibrium is achieved; the concentrations of reactant and products become constant.

Answer 6

Chapter 10.3, Problem 5PTS

(a)

Interpretation Introduction

Interpretation:

For the given set of reactions the base present in each reaction should be identified that if it is sufficient to deprotonate the terminal alkyne.

Concept Introduction:

Acid-Base Reaction: This type of chemical process typified by the exchange of one or more hydrogens ions H⁺, between species that may be neutral molecules or electrically charged ions.

Chemical equilibrium: The term applied to reversible chemical reactions. It is the point at which the rate of the forward reaction is equal to the rate of the reverse reaction. The equilibrium is achieved; the concentrations of reactant and products become constant.

Answer 7

Chapter 10.3, Problem 5PTS

(a)

Interpretation Introduction

Interpretation:

For the given set of reactions the base present in each reaction should be identified that if it is sufficient to deprotonate the terminal alkyne.

Concept Introduction:

Acid-Base Reaction: This type of chemical process typified by the exchange of one or more hydrogens ions H⁺, between species that may be neutral molecules or electrically charged ions.

Chemical equilibrium: The term applied to reversible chemical reactions. It is the point at which the rate of the forward reaction is equal to the rate of the reverse reaction. The equilibrium is achieved; the concentrations of reactant and products become constant.

Answer 8

(b)

Interpretation Introduction

Interpretation:

For the given set of reactions the base present in each reaction should be identified that if it is sufficient to deprotonate the terminal alkyne.

Concept Introduction:

Acid-Base Reaction: This type of chemical process typified by the exchange of one or more hydrogens ions H⁺, between species that may be neutral molecules or electrically charged ions.

Chemical equilibrium: The term applied to reversible chemical reactions. It is the point at which the rate of the forward reaction is equal to the rate of the reverse reaction. The equilibrium is achieved; the concentrations of reactant and products become constant.

Answer 9

(b)

Interpretation Introduction

Interpretation:

For the given set of reactions the base present in each reaction should be identified that if it is sufficient to deprotonate the terminal alkyne.

Concept Introduction:

Acid-Base Reaction: This type of chemical process typified by the exchange of one or more hydrogens ions H⁺, between species that may be neutral molecules or electrically charged ions.

Chemical equilibrium: The term applied to reversible chemical reactions. It is the point at which the rate of the forward reaction is equal to the rate of the reverse reaction. The equilibrium is achieved; the concentrations of reactant and products become constant.

Answer 10

(c)

Interpretation Introduction

Interpretation:

For the given set of reactions the base present in each reaction should be identified that if it is sufficient to deprotonate the terminal alkyne.

Concept Introduction:

Acid-Base Reaction: This type of chemical process typified by the exchange of one or more hydrogens ions H⁺, between species that may be neutral molecules or electrically charged ions.

Chemical equilibrium: The term applied to reversible chemical reactions. It is the point at which the rate of the forward reaction is equal to the rate of the reverse reaction. The equilibrium is achieved; the concentrations of reactant and products become constant.

Answer 11

(c)

Interpretation Introduction

Interpretation:

For the given set of reactions the base present in each reaction should be identified that if it is sufficient to deprotonate the terminal alkyne.

Concept Introduction:

Acid-Base Reaction: This type of chemical process typified by the exchange of one or more hydrogens ions H⁺, between species that may be neutral molecules or electrically charged ions.

Chemical equilibrium: The term applied to reversible chemical reactions. It is the point at which the rate of the forward reaction is equal to the rate of the reverse reaction. The equilibrium is achieved; the concentrations of reactant and products become constant.

Answer 12

(d)

Interpretation Introduction

Interpretation:

For the given set of reactions the base present in each reaction should be identified that if it is sufficient to deprotonate the terminal alkyne.

Concept Introduction:

Acid-Base Reaction: This type of chemical process typified by the exchange of one or more hydrogens ions H⁺, between species that may be neutral molecules or electrically charged ions.

Chemical equilibrium: The term applied to reversible chemical reactions. It is the point at which the rate of the forward reaction is equal to the rate of the reverse reaction. The equilibrium is achieved; the concentrations of reactant and products become constant.

Answer 13

(d)

Interpretation Introduction

Interpretation:

For the given set of reactions the base present in each reaction should be identified that if it is sufficient to deprotonate the terminal alkyne.

Concept Introduction:

Acid-Base Reaction: This type of chemical process typified by the exchange of one or more hydrogens ions H⁺, between species that may be neutral molecules or electrically charged ions.

Chemical equilibrium: The term applied to reversible chemical reactions. It is the point at which the rate of the forward reaction is equal to the rate of the reverse reaction. The equilibrium is achieved; the concentrations of reactant and products become constant.

Answer 14

(e).

Interpretation Introduction

Interpretation:

For the given set of reactions the base present in each reaction should be identified that if it is sufficient to deprotonate the terminal alkyne.

Concept Introduction:

Acid-Base Reaction: This type of chemical process typified by the exchange of one or more hydrogens ions H⁺, between species that may be neutral molecules or electrically charged ions.

Chemical equilibrium: The term applied to reversible chemical reactions. It is the point at which the rate of the forward reaction is equal to the rate of the reverse reaction. The equilibrium is achieved; the concentrations of reactant and products become constant.

Answer 15

(e).

Interpretation Introduction

Interpretation:

For the given set of reactions the base present in each reaction should be identified that if it is sufficient to deprotonate the terminal alkyne.

Concept Introduction:

Acid-Base Reaction: This type of chemical process typified by the exchange of one or more hydrogens ions H⁺, between species that may be neutral molecules or electrically charged ions.

Chemical equilibrium: The term applied to reversible chemical reactions. It is the point at which the rate of the forward reaction is equal to the rate of the reverse reaction. The equilibrium is achieved; the concentrations of reactant and products become constant.

Answer 16

(f).

Interpretation Introduction

Interpretation:

For the given set of reactions the base present in each reaction should be identified that if it is sufficient to deprotonate the terminal alkyne.

Concept Introduction:

Acid-Base Reaction: This type of chemical process typified by the exchange of one or more hydrogens ions H⁺, between species that may be neutral molecules or electrically charged ions.

Chemical equilibrium: The term applied to reversible chemical reactions. It is the point at which the rate of the forward reaction is equal to the rate of the reverse reaction. The equilibrium is achieved; the concentrations of reactant and products become constant.

Answer 17

(f).

Interpretation Introduction

Interpretation:

For the given set of reactions the base present in each reaction should be identified that if it is sufficient to deprotonate the terminal alkyne.

Concept Introduction:

Acid-Base Reaction: This type of chemical process typified by the exchange of one or more hydrogens ions H⁺, between species that may be neutral molecules or electrically charged ions.

Chemical equilibrium: The term applied to reversible chemical reactions. It is the point at which the rate of the forward reaction is equal to the rate of the reverse reaction. The equilibrium is achieved; the concentrations of reactant and products become constant.

Answer 18

Expert Solution & Answer

Answer 19

Expert Solution & Answer

Answer 20

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 21

Ch. 10.2 - Prob. 1LTS Ch. 10.2 - Prob. 1PTS Ch. 10.2 - Prob. 2ATS Ch. 10.2 - Prob. 3ATS Ch. 10.2 - Prob. 4ATS Ch. 10.3 - Prob. 2LTS Ch. 10.3 - Prob. 5PTS Ch. 10.3 - Prob. 6ATS Ch. 10.4 - Prob. 7CC Ch. 10.4 - Prob. 8CC

Want to see the full answer?

Chapter 10 Solutions