Question

a flexible container holds 97.4 liters of hydrogen gas (h₂). after the gas is cooled to -8.6°c, it occupies a final volume of 81.3 liters. what was the initial temperature of the h₂ gas before it was cooled? assume ideal gas behavior and a constant pressure. write your answer to the correct number of significant figures. round if necessary. °c submit

Explanation:

Step1: Convert final temp to Kelvin

$T_2 = -8.6^\circ\text{C} + 273.15 = 264.55\ \text{K}$

Step2: Apply Charles's Law

Charles's Law: $\frac{V_1}{T_1} = \frac{V_2}{T_2}$, rearrange to solve for $T_1$:
$T_1 = \frac{V_1 \times T_2}{V_2}$
Substitute values: $T_1 = \frac{97.4\ \text{L} \times 264.55\ \text{K}}{81.3\ \text{L}}$

Step3: Calculate initial temp in Kelvin

$T_1 = \frac{97.4 \times 264.55}{81.3} \approx 316.9\ \text{K}$

Step4: Convert back to Celsius

$T_1 = 316.9\ \text{K} - 273.15 = 43.75^\circ\text{C}$

Step5: Round to sig figs

Round to 3 significant figures: $43.8^\circ\text{C}$

Answer:

$43.8$