Question

a gas - ion has a volume of 3.2 liters when the temperature is 12.9 °c and the pressure is 705.0 mm of mercury. what will its volume be in l at 24.8 °c and 782 mm of mercury? express your answer with 1 decimal place.

Explanation:

Step1: Convert temperatures to Kelvin

$T_1 = 12.9+273.15=286.05\ K$, $T_2 = 24.8 + 273.15=297.95\ K$

Step2: Apply the combined - gas law $\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}$

We know $P_1 = 705.0\ mmHg$, $V_1 = 3.2\ L$, $P_2 = 782\ mmHg$, $T_1$ and $T_2$ from Step 1. Rearranging for $V_2$ gives $V_2=\frac{P_1V_1T_2}{P_2T_1}$

Step3: Substitute values and calculate

$V_2=\frac{705.0\times3.2\times297.95}{782\times286.05}$
$V_2=\frac{705.0\times3.2\times297.95}{782\times286.05}\approx2.9\ L$

Answer:

$2.9$