## Chapter 12

## Q. 12.11

**Calculating the Volume of a Gas Using the Ideal Gas Law**

The colorless, odorless, tasteless, toxic gas carbon monoxide, CO, is a by-product of incomplete combustion of any material that contains the element carbon. Calculate the volume, in liters, occupied by 1.52 moles of this gas at 0.992 atm pressure and a temperature of 65°C.

## Step-by-Step

## Verified Solution

This problem deals with only one set of conditions, a situation w here the ideal gas equation is applicable. Three of the four variables in the ideal gas equation (P, n, and T) are given, and the fourth (*V*) is to be calculated.

*P* = 0.992 atm *n* = 1.52 moles

*V* = ? L*T* = 65°C = 338 K

Rearranging the ideal gas equation to isolate V on the left side of the equation gives

V = \frac{nRT}{P}Since the pressure is given in atmospheres and the volume unit is in liters, the appropriate R value is

R = 0.08206 \frac{\textrm{atm} \cdot \textrm{L}}{\textrm{mole} \cdot \textrm{K}}Substituting the given numerical values into the equation and cancelling units gives

V = \frac{(1.52 \cancel{\textrm{moles}}) \Bigl(0.08206 \frac{ \cancel{\textrm{atm}} \cdot \textrm{L}}{\cancel{\textrm{mole}} \cdot \cancel{\textrm{K}}} \Bigr) (338 \cancel{\textrm{K}})}{0.992 \cancel{\textrm{atm}}}Note how all of the parts of the ideal gas constant unit system cancel except for one, the volume part.

Doing the arithmetic, we get as an answer 42.5 L CO.

V = \frac{1.52 \times 0.08206 \times 338}{0.992} L CO

= 42.499138 L CO (calculator answer)

**= 42.5 L CO (correct answer)**

**Answer Double Check**: Is the ideal gas law, in its rearranged form, in a form such that all of the units cancel except for that of volume (liters)? The answer is yes.