Question

a sample of carbon dioxide gas (co₂) with a volume of 0.3745 cubic meters is heated to 15.7°c. after heating, the gas occupies a final volume of 0.3918 cubic meters. what was the initial temperature of the co₂ gas before it was heated? assume ideal gas behavior and a constant pressure. write your answer to the correct number of significant figures. round if necessary. \boxed{} °c save answer

Explanation:

Step1: Recall Charles's Law

Charles's Law states that for a gas at constant pressure, $\frac{V_1}{T_1}=\frac{V_2}{T_2}$, where $V_1$ and $V_2$ are initial and final volumes, and $T_1$ and $T_2$ are initial and final absolute temperatures (in Kelvin).

Step2: Convert final temperature to Kelvin

The final temperature $T_2 = 15.7^\circ\text{C}+ 273.15=288.85\ \text{K}$.

Step3: Rearrange Charles's Law to solve for $T_1$

From $\frac{V_1}{T_1}=\frac{V_2}{T_2}$, we get $T_1=\frac{V_1\times T_2}{V_2}$. Substitute $V_1 = 0.3745\ \text{m}^3$, $V_2=0.3918\ \text{m}^3$, and $T_2 = 288.85\ \text{K}$:
$T_1=\frac{0.3745\times288.85}{0.3918}\approx\frac{108.2}{0.3918}\approx276.95\ \text{K}$.

Step4: Convert $T_1$ back to Celsius

To convert Kelvin to Celsius, use $T(\text{°C})=T(\text{K}) - 273.15$. So, $T_1(\text{°C})=276.95 - 273.15 = - 4.2\ \text{°C}$ (rounded to two significant figures, or considering the precision of given values).

Answer:

-4.2