Question

In Figure P5.10, what is the pressure of the gas in the flask (in atm) if the barometer reads 738.5 torr?

Short answer

The pressure of the gas is 0.941 atm.

Step-by-step solution

Total pressure

Total pressure is the sum of the pressure of the atmosphere and the difference in heights of the columns.

Determination of pressure of the gas

Convert the total pressure from torr to mmHg.

$\begin{array}{rcl}& & \text{1} \text{torr} \text{=} \text{1} \text{mmHg}\\ & \Rightarrow & \text{738.5} \text{torr} \text{= 738.5} \text{mmHg}\\ & & \end{array}$

Convert cmHg to mmHg

$$\begin{gathered} \text{1} \text{cmHg} \text{=} \text{10} \text{mmHg} \\ \Rightarrow \text{2.35} \text{cmHg} \text{=} \text{23.5} \text{mmHg} \end{gathered}$$

Now, the pressure of the gas is,

$\begin{array}{rcl}& & {\text{P}}_{\text{total}}{\text{=∆h+P}}_{\text{gas}}\\ & & {\text{P}}_{\text{gas} }\text{=} {\text{P}}_{\text{total} }\text{-∆h}\\ & & \text{= 738.5} \text{mmHg} \text{-} \text{23.5} \text{mmHg}\\ & & \text{=} \text{715} \text{mmHg}\\ & & \end{array}$

Now, convert the pressure of the gas from mmHg to atm,

1 atm = 760 mmHg

$\text{715} \text{mmHg} \times \frac{\text{1} \text{atm}}{\text{760} \text{mmHg}} \text{=} \text{0.941} \text{atm}$

Thus, the pressure of the gas is 0.941 atm.