Question

(2) choose the best answer.
a 54.0 ml sample of hydrogen gas is collected at 23.0 °c and 770 mmhg pressure. what is the volume at stp (0.0 °c and 760 mmhg)?
59.3 ml
50.5 ml
90.2 ml

Explanation:

Step1: Convert units to SI/STP standards

Convert temperatures to Kelvin:
$T_1 = 23.0^\circ\text{C} + 273.15 = 296.15\ \text{K}$
$T_2 = 0.0^\circ\text{C} + 273.15 = 273.15\ \text{K}$
Given values:
$V_1 = 54.0\ \text{mL}$, $P_1 = 770\ \text{mmHg}$, $P_2 = 760\ \text{mmHg}$

Step2: Apply combined gas law

Use $\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$, solve for $V_2$:
$V_2 = \frac{P_1V_1T_2}{P_2T_1}$

Step3: Substitute values and calculate

$$ V_2 = \frac{770\ \text{mmHg} \times 54.0\ \text{mL} \times 273.15\ \text{K}}{760\ \text{mmHg} \times 296.15\ \text{K}} $$

$V_2 \approx 50.5\ \text{mL}$

Answer:

50.5 mL