Chapter 6, Problem 1SAQ

How many atoms are there in 5.8 mol helium?

a. 23.2 atoms

b. $\text{9}\text{.6 }\times {\text{ 10}}^{\text{-24}}$ atoms

c. $\text{5}\text{.8 }\times {\text{ 10}}^{\text{23}}$ atoms

d. $\text{3}\text{.5 }\times {\text{ 10}}^{\text{24}}$ atoms

Interpretation Introduction

Interpretation: The number of atoms in $5.8\text{ mol}$ helium is to be calculated.

Concept Introduction: One mole of the substance contains $6.022\times {10}^{23}\text{ atoms}\text{.}$ Thus, to convert between moles of an element and number of atoms, use the following conversion factor:$\frac{1\text{ mol}}{6.022\times {10}^{23}\text{atoms}}\text{or}\frac{6.022\times {10}^{23}\text{atoms}}{1\text{ mol}}$

Answer to Problem 1SAQ

Correct Answer: Thenumber of atoms in $5.8\text{ mol}$ of helium is $3.5\times {10}^{24}.$ Therefore, option (d) is correct.

Explanation of Solution

Reason for correct option:

In order to carry out the conversions between moles of atoms and number of atoms, use the conversion factor as follows:

$\frac{6.022\times {10}^{23}\text{atoms}}{1\text{ mol}}$

To determine the number of helium atoms present in $5.8\text{ mol}$ of helium, multiply the conversion factor with $5.8\text{ mol}$.

$\begin{array}{c}\text{Number}\text{of}\text{atoms}\text{in}\text{5}\text{.8 mol of He}=5.8\cancel{\text{mol He}}\times \frac{6.022\times {10}^{23}\text{atoms}}{1\cancel{\text{mol He}}}\\ =34.9\times {10}^{23}\text{atoms}\end{array}$

As the given value is in two significant figures, the final answer should also be in two significant figures.Roundoff the answer to two significant figures; hence, the answer is $3.5\times {10}^{24}\text{atoms}$.

Hence, option (d) is correct.

Reasons for incorrect options:

Option (a)is incorrect because according to the above relation, the value $23.2\text{ atoms}$ cannot be obtained. So, it is a wrong answer.

Option (b) is incorrect because the value $9.6\times {10}^{-24}\text{ atoms}$ cannot be obtained according to the above relation. So, it is a wrong answer.

Option (c)is incorrect as per the above relation. The value $5.8\times {10}^{23}\text{ atoms}$ cannot be obtained. So, it is a wrong answer.

Hence, options (a), (b), and (c) are incorrect.