# A volume of hydrogen gas is collected over water in an investigation. If the atmospheric pressure is 102.1 kPa and the pressure of the hydrogen gas is 100.1 kPa, what temperature is the water?

## The answer is [ans: 17.5 °C] but I don't know exactly how to get to that answer

Jul 4, 2018

The above table presents different values of pressures of saturated water vapour at different temperatures.

In our problem hydrogen gas has been collected over water. So total pressure (${P}_{\text{total}}$) of the collected gas is sum of the pressure of dry gas (${P}_{\text{Hy}}$)and aqueous tension (${P}_{\text{aq}}$).

So ${P}_{\text{total"=P_"Hy"+P_"aw}}$

By the problem
${P}_{\text{total"="atmospheric pressure}} = 102.1$kPa

${P}_{\text{Hy}} = 100.1$kPa

P_"aw"=?

So

${P}_{\text{aw}} = 2$ kPa

Now from table we get

At ${18}^{\circ} C$ aqueous tension =2.06 kPa

And

At ${16}^{\circ} C$ aqueous tension =1.81 kPa

This shows that aqueous tension falls by 0.25kPa when temperature falls by ${2}^{\circ} C$

So fall of $2.06 - 2 = 0.06$ kPa pressure will occur due to fall of temperature by $\frac{2}{0.25} \times 0.06 \approx {0.5}^{\circ} C$

So the temperature of the collected gas should be$= 18 - 0.5 = {17.5}^{\circ} C$