Question

a flexible container holds 5.30 liters of nitrogen gas ($ce{n_2}$) at $17.28^circ$c. the gas is heated until it occupies a final volume of 5.76 liters. what is the final temperature of the $ce{n_2}$ gas after it is heated? assume ideal gas behavior and a constant pressure.
write your answer to the correct number of significant figures. round if necessary.
$square$ $^circ$c
submit

Explanation:

Step1: Convert temp to Kelvin

$T_1 = 17.28 + 273.15 = 290.43\ \text{K}$

Step2: Apply Charles's Law

$\frac{V_1}{T_1} = \frac{V_2}{T_2} \implies T_2 = \frac{V_2 \times T_1}{V_1}$

Step3: Substitute values

$T_2 = \frac{5.76\ \text{L} \times 290.43\ \text{K}}{5.30\ \text{L}} \approx 314.39\ \text{K}$

Step4: Convert back to °C

$T_2 = 314.39 - 273.15 = 41.24\ \text{°C}$

Step5: Round to sig figs

Round to 3 significant figures: $41.2\ \text{°C}$

Answer:

$41.2$ °C