Question

a syringe containing 1.75 ml of oxygen gas is cooled from 92.3 °c to 0.1 °c. what is the final volume vf of oxygen gas? (assume that the pressure is constant.)

Explanation:

Step1: Convert temperatures to Kelvin

Charles's Law ($\frac{V_1}{T_1}=\frac{V_2}{T_2}$) requires temperatures in Kelvin.
$T_1 = 92.3+273.15=365.45\ \text{K}$, $T_2 = 0.1 + 273.15=273.25\ \text{K}$, $V_1=1.75\ \text{mL}$

Step2: Rearrange Charles's Law to solve for $V_2$

From $\frac{V_1}{T_1}=\frac{V_2}{T_2}$, we get $V_2=\frac{V_1T_2}{T_1}$
Substitute values: $V_2=\frac{1.75\times273.25}{365.45}$

Step3: Calculate $V_2$

$V_2=\frac{478.1875}{365.45}\approx1.31\ \text{mL}$

Answer:

$1.31$