If a gas sample has a pressure of 30.7 kPa at 0.00°C, by how much does the temperature have to decrease to lower the pressure to 28.4 kPa?

Mar 16, 2016

${T}_{2} = - {20.5}^{\circ} \text{C}$

Explanation:

In this question I assume that the volume is unchanged and therefore, we can use the following law:

$\frac{P}{T} = k$

Then, $\frac{{P}_{1}}{{T}_{1}} = \frac{{P}_{2}}{{T}_{2}} \implies {T}_{2} = \frac{{T}_{1}}{{P}_{1}} \times {P}_{2}$

=>P_2=("273.15 K")/(30.7cancel("kPa"))xx28.4cancel("kPa") = "252.69 K"

Therefore, the temperature should be lowered to: $252.69 - 273.15 = - {20.464}^{\circ} \text{C}$

$\implies \textcolor{b l u e}{{T}_{2} = - {20.5}^{\circ} \text{C}}$ to 3 sig figs.