a gas system is cooled from 38.1 °c to 15.0 °...

a gas system is cooled from 38.1 °c to 15.0 °c. what is the initial volume of the system if the final volume is 4.50 l? v = ? l assume that the number of moles and the pressure remain constant.

Answer

# Explanation: ## Step1: Convert temperatures to Kelvin Initial temperature $T_1=(38.1 + 273.15)\text{ K}=311.25\text{ K}$, final temperature $T_2=(15.0+ 273.15)\text{ K}=288.15\text{ K}$, final volume $V_2 = 4.50\text{ L}$. ## Step2: Apply Charles's Law ($\frac{V_1}{T_1}=\frac{V_2}{T_2}$) $V_1=\frac{V_2T_1}{T_2}$ ## Step3: Substitute values $V_1=\frac{4.50\text{ L}\times311.25\text{ K}}{288.15\text{ K}}$ $V_1=\frac{1390.625}{288.15}\text{ L}\approx4.826\text{ L}$ # Answer: $4.83\text{ L}$ (rounded to two - decimal places)