Q5.10P - Chemistry: Molecular Nature Of Matter And Change

Question

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

Step-by-Step Solution

Answer

The pressure of the gas is 0.941 atm.

Step 1: Total pressure

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

Step 2: 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.