Question

In Figure P5.11, what is the pressure of the gas in the flask (in kPa) if the barometer reads 765.2 mmHg?

Short answer

The pressure of the gas is 100.0 kPa.

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 cmHg to mmHg

$$\begin{gathered} \text{1} \text{cmHg} \text{=} \text{10} \text{mmHg} \\ \Rightarrow 1.3 \text{cmHg} \text{=} 13 \text{mmHg} \end{gathered}$$

The pressure of the gas is,

$\begin{array}{rcl}& & {\text{P}}_{\text{total}}\text{=∆h+} {\text{P}}_{\text{gas}}\\ & & {\text{P}}_{\text{gas} }\text{=} {\text{P}}_{\text{total} }-∆h\\ & & \text{= 765.2} \text{mmHg} \text{-} 13 \text{mmHg}\\ & & \text{=} \text{752.2} \text{mmHg}\\ & & \end{array}$

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

1 mmHg = 0.133 kPa

$\text{752.2} \text{mmHg×}\frac{0.133 \text{kPa}}{1 \text{mmHg}} \text{=} 100.0 \text{kPa}$

Thus, the pressure of the gas is 100.0 kPa.