Chapter 5, Problem 26P

Interpretation Introduction

(a)

Interpretation:

Find if the given statement is true or false.

“Avogadro’s law states that equal volume of gas at the same temperature and pressure contain equal number of molecules”.

Concept Introduction:

According to Avogadro’s law states that equal volume of gas at the same temperature and pressure contain equal number of molecules.

Answer to Problem 26P

Avogadro’s law states that equal volume of gas at the same temperature and pressure contain equal number of molecules. Thus, the given statement is true.

Explanation of Solution

Given information:

Avogadro’s law states that equal volume of gas at the same temperature and pressure contain equal number of molecules.

According to the Avogadro’s law, equal volume of gas at the same temperature and pressure contain equal number of molecules.

Interpretation Introduction

(b)

Interpretation:

Find if the given statement is true or false.

“At STP, one mole of uranium hexafluoride occupies a volume of $352\text{ L}$.”

Concept Introduction:

Mathematically, Ideal gas law states that:

$PV=nRT$

Where,

$P=$ Pressure of the gas in atmospheres ($\text{a}\text{t}\text{m}$).

$V=$ Volume of the gas in litres ($\text{l}$).

$n=$ Amount of the gas in moles ($m\text{O}\text{l}$).

$R=$ Ideal gas constant.

$T=$ Temperature of the gas in kelvins ($K$).

Answer to Problem 26P

At STP, one mole of uranium hexafluoride occupies a volume of $22.4\text{ L}$. Thus, the given statement is false.

Explanation of Solution

At STP, $T=273.15\text{ K}$, $P=1\text{atm}$, $R=0.0821\text{L}\text{.atm}{\text{.mol}}^{-1}.{\text{K}}^{-1}$ and $n=1$

We know that, as per ideal gas law, $PV=nRT$

Now, we need to calculate volume.

Substituting the values, we get.

$\left(1\text{atm}\right)V=\left(1\text{mol}\right)\left(0.0821\text{L}\text{.atm}{\text{.mol}}^{-1}.{\text{K}}^{-1}\right)\left(273.15\text{K}\right)$

$V=\frac{\left(1\text{mol}\right)\left(0.0821\text{L}\text{.atm}{\text{.mol}}^{-1}.{\text{K}}^{-1}\right)\left(273.15\text{K}\right)}{\left(1\text{atm}\right)}$

$V=22.4\text{l}$

Hence, at STP, one mole of uranium hexafluoride occupies a volume of $22.\text{4 L}$.

Interpretation Introduction

(c)

Interpretation:

Find if the given statement is true or false.

“If two gas samples have the same temperature, volume and pressure, the both contain same number of molecules.”

Concept Introduction:

Avogadro’s law states that equal volume of gas at the same temperature and pressure contain equal number of molecules.

Answer to Problem 26P

If two gas samples have the same temperature, volume and pressure, the both contain same number of molecules. Thus, the given statement is true.

Explanation of Solution

According to Avogadro’s law, equal volume of gas at the same temperature and pressure contain equal number of molecules. Thus, if two gas samples have the same temperature, volume and pressure, the both contain same number of molecules.

Interpretation Introduction

(d)

Interpretation:

Find if the given statement is true or false.

“The value of Avogadro’s number is $6.02\times {10}^{23}\text{ g/}m\text{O}\text{l}$”.

Concept Introduction:

Avogadro’s law states that equal volume of gas at the same temperature and pressure contain equal number of molecules.

Answer to Problem 26P

The value of Avogadro’s number is $6.02\times {10}^{23}{\text{ unit mol}}^{-1}$. Thus, the given statement is false.

Explanation of Solution

Avogadro’s number is defined as number of units in 1 mole of a substance. According to Avogadro’s law, there are $6.02\times {10}^{23}\text{ atoms}$ of substance in 1 mol of that substance. Similarly, for a molecule, 1 mol contains $6.02\times {10}^{23}\text{ molecules}$ of the substance.

Thus, Avogadro’s number is equal to $6.02\times {10}^{23}{\text{ unit mol}}^{-1}$.

Interpretation Introduction

(e)

Interpretation:

Find if the given statement is true or false.

“Avogadro’s number is valid only for gases at STP.”

Concept Introduction:

Avogadro’s number is a total number of units in one mole of any substance.

Avogadro’s number is equal to $6.02\times {10}^{23}{\text{ mol}}^{-1}$.

Answer to Problem 26P

Avogadro’s number is valid for gases at any temperature or pressure value. Thus, the given statement is false.

Explanation of Solution

Avogadro’s law states that equal volume of gas at the same temperature and pressure contain equal number of molecules.

At any temperature or pressure value, the number of atoms or molecules in one mol of a substance is equal to Avogadro’s number that is $6.02\times {10}^{23}$.

Interpretation Introduction

(f)

Interpretation:

Find if the given statement is true or false.

“The ideal gas law is $PV=nRT$ ”.

Concept Introduction:

Mathematically, Ideal gas law states that:

$PV=nRT$

Where,

$P=$ Pressure of the gas in atmospheres ($\text{a}\text{t}\text{m}$).

$V=$ Volume of the gas in litres ($\text{l}$).

$n=$ Amount of the gas in moles ($m\text{O}\text{l}$).

$R=$ Ideal gas constant.

$T=$ Temperature of the gas in kelvins ($K$).

Answer to Problem 26P

The ideal gas law is $PV=nRT$. Thus, the given statement is true.

Explanation of Solution

Given information:

The ideal gas law is $PV=nRT$

Mathematically, Ideal gas law states that:

$PV=nRT$.

Interpretation Introduction

(g)

Interpretation:

Find if the given statement is true or false.

“When using the ideal gas law for calculations, temperature must be in degrees Celsius.”

Concept Introduction:

Mathematically, Ideal gas law states that:

$PV=nRT$

Where,

$P=$ Pressure of the gas in atmospheres ($\text{a}\text{t}\text{m}$).

$V=$ Volume of the gas in litres ($\text{l}$).

$n=$ Amount of the gas in moles ($m\text{O}\text{l}$).

$R=$ Ideal gas constant.

$T=$ Temperature of the gas in kelvins ($K$).

Answer to Problem 26P

When using the ideal gas law for calculations, temperature must be in Kelvin. Thus, the given statement is False.

Explanation of Solution

When we are using ideal gas law for calculations, temperature must be in Kelvin. The temperature can never be in Celsius. This is because $0^{\circ }\text{C}$ will result in wrong answer and it corresponds to $273.15K$, which will give the correct answer.

Interpretation Introduction

(h)

Interpretation:

Find if the given statement is true or false.

“If one mole of ethane gas occupies $20.\text{0 L}$ at $1.00\text{a}\text{t}\text{m}$, the temperature of the gas is $244\mathrm{K}$ ”.

Concept Introduction:

Mathematically, Ideal gas law states that:

$PV=nRT$

Where,

$P=$ Pressure of the gas in atmospheres ($\text{a}\text{t}\text{m}$).

$V=$ Volume of the gas in litres ($\text{l}$).

$n=$ Amount of the gas in moles ($m\text{O}\text{l}$).

$R=$ Ideal gas constant.

$T=$ Temperature of the gas in kelvins ($K$).

Answer to Problem 26P

If one mole of ethane gas occupies $20.\text{0 L}$ at $1.00\text{a}\text{t}\text{m}$, the temperature of the gas is $244\mathrm{K}$. Thus, the given statement is true.

Explanation of Solution

We have $P=\text{1atm}$, $V=20.0\text{L}$ and $R=0.0821\text{L}\text{.atm}{\text{.mol}}^{-1}.{\text{K}}^{-1}$, $n=1$

We know that, as per ideal gas law, $PV=nRT$

Now, we need to calculate volume.

Substituting the values, we get.

$\left(1\text{atm}\right)\left(20.0\text{L}\right)=\left(1\text{mol}\right)\left(0.0821\text{ L}\text{.atm}{\text{.mol}}^{-1}.{\text{K}}^{-1}\right)T$

$T=\frac{\left(\text{1 atm}\right)\left(20.0\text{ L}\right)}{\left(1\text{ mol}\right)\left(0.082\text{1 L}\text{.atm}{\text{.mol}}^{-1}.{\text{K}}^{-1}\right)}$

$T=243.6\text{K}\approx 244\text{K}$

Hence, if one mole of ethane gas occupies $20.\text{0 L}$ at $1.00\text{ atm}$, the temperature of the gas is $24\text{4 K}$.

Interpretation Introduction

(i)

Interpretation:

Find if the given statement is true or false.

“One mole of helium gas at STP occupies twice the volume of one mole of hydrogen”.

Concept Introduction:

According to Avogadro’s law states that equal volume of gas at the same temperature and pressure contain equal number of molecules.

Answer to Problem 26P

One mole of helium gas at STP occupies same the volume of one mole of hydrogen. Thus, the given statement is false.

Explanation of Solution

Given information:

One mole of helium gas at STP occupies twice the volume of one mole of hydrogen

According to Avogadro’s law, equal volume of gas at the same temperature and pressure contain equal number of molecules We have one mole of helium gas at STP and one mole of hydrogen gas at STP.

One mole of any substance will occupy $22.\text{4 L}$.