# Question 1231e

Apr 10, 2017

671.4mL to 1 decimal place.

#### Explanation:

As temperature and number of moles of gas remained unchanged, use the formula ${P}_{1} \cdot {V}_{1} = {P}_{2} \cdot {V}_{2}$, where ${P}_{1}$ and ${P}_{2}$ are the old and new pressures and ${V}_{1}$ and ${V}_{2}$ are the old and new volumes respectively, to calculate the volume of gas.

You must convert the pressures into a single unit. The best option is to convert the new pressure, given in mmHg, into atm. As we know, $1 a t m = 760 m m H g$
Therefore, $738 m m H g = \frac{738}{760} a t m$. For the sake of accuracy, we are going to used this fraction rather than the irrational decimal value.
${P}_{1} \cdot {V}_{1} = {P}_{2} \cdot {V}_{2}$
${P}_{1} = 1 a t m$
${V}_{1} = 652 m L$
${P}_{2} = \frac{738}{760} a t m$
V_2 = ?#

Putting in all the known values, we have:
$1 a t m \cdot 652 m L = \frac{738}{760} a t m \cdot {V}_{2} m L$
${V}_{2} = \frac{1 a t m \cdot 652 m L}{\frac{738}{760} a t m}$
${V}_{2} = 671.436 m L$