Chapter 3, Problem 1QAP

One chocolate chip used in making chocolate chip cookies has a mass of 0.324 g.

(a) How many chocolate chips are there in one mole of chocolate chips?

(b) If a cookie needs IS chocolate chips, how many cookies can one make with a billionth $\left(1\times {10}^{-9}\right)$ of a mole of chocolate chips? (A billionth of a mole is scientifically known as a nanomole.)

Interpretation Introduction

(a)

Interpretation:

The number of chocolate chips there in 1 mol of chocolate chips should be calculated.

Concept introduction:

The number of moles of a substance is related to molar mass of the substance as follows:

$n=\frac{m}{M}$

Here, m is mass and M is molar mass.

According to Avogadro’s law, in 1 mol of a substance there are $6.023\times {10}^{23}$ units of that substance.

Also, density of a substance is related to mass and volume as follows:

$d=\frac{m}{V}$

Here, m is mass and V is volume of the substance.

Answer to Problem 1QAP

$6.023\times {10}^{23}$

Explanation of Solution

According to Avogadro’s law, 1 mol of a substance contains $6.023\times {10}^{23}$ units of that substance. Here, $6.023\times {10}^{23}$ is known as Avogadro’s number and denoted by symbol $N_A$.

Thus, according to Avogadro’s law, in 1 mol of chocolate chips there are $6.023\times {10}^{23}$ chocolate chips.

Interpretation Introduction

(b)

Interpretation:

The number of cookies in a billionth mol of chocolate chips should be calculated.

Concept introduction:

The number of moles of a substance is related to molar mass of the substance as follows:

$n=\frac{m}{M}$

Here, m is mass and M is molar mass.

According to Avogadro’s law, in 1 mol of a substance there are $6.023\times {10}^{23}$ units of that substance.

Answer to Problem 1QAP

$4.015\times {10}^{13}$

Explanation of Solution

If making of 1 cookie needs 15 chocolate chips. The number of cookies that can be made from $1\times {10}^{-9}$ mole of chocolate chips should be calculated.

Since, 1 mol of chocolate chips contain $6.023\times {10}^{23}$ chocolate chips thus, number of chocolate chips in $1\times {10}^{-9}$ moles can be calculated as follows:

$\begin{array}{c}n=\left(\frac{6.023\times {10}^{23}}{1\text{ mol}}\right)\left(1\times {10}^{-9}\text{ mol}\right)\\ =6.023\times {10}^{14}\end{array}$

Now, 15 chocolate chips are used in making of 1 cookie and 1 chocolate chip is used in making $\frac{1}{15}$ cookie. Thus, number of cookies made from $6.023\times {10}^{14}$ chocolate chips will be:

$\begin{array}{c}N=6.023\times {10}^{14}\left(\frac{1}{15}\right)\\ =4.015\times {10}^{13}\end{array}$

Therefore, number of cookies is $4.015\times {10}^{13}$.