Question 6.10: Automotive airbags inflate when sodium azide, NaN3, rapidly ......
Automotive airbags inflate when sodium azide, NaN_{3}, rapidly decomposes to its constituent elements. The equation for the chemical reaction is
\quad\quad\quad\quad 2NaN_{3}(s) → 2Na(s) + 3N_{2}(g)
The gaseous N_2 so generated inflates the airbag (see Figure 6.10). How many moles of NaN_{3} would have to decompose in order to generate 253 million (2.53 × 10^{8}) molecules of N_2?
Although a calculation of this type does not have a lot of practical significance, it tests your understanding of the problem-solving relationships discussed in this section of the text.
Step 1: The given quantity is 2.53 × 10^{8} molecules of N_2, and the desired quantity is moles of NaN_{3}.
\quad\quad\quad\quad2.53 × 10^{8} molecules N_2 = ? moles NaN_{3}
In terms of Figure 6.9, this is a “particles of A” to “moles of B” problem.
Step 2: Using Figure 6.9 as a road map, we determine that the pathway for this problem is
The mathematical setup is
\quad\quad 2.53\times 10^{8} \cancel{molecules N_{2}}\times (\frac{1 \cancel{mole N_{2}}}{6.02\times 10^{23} \cancel{molecules N_{2}}})\times (\frac{2 \cancel{moles NaN_{3}}}{3 \cancel{moles N_{2}}})Avogadro’s number is present in the first conversion factor. The 2 and 3 in the second conversion factor are the coefficients, respectively, of NaN_{3} and N_2 in the balanced chemical equation.
Step 3: The solution to the problem, obtained by doing the arithmetic after all the numerical factors have been collected, is
