Question

1. a 48.3-ml sample of gas in a cylinder is warmed from 22 °c to 87 °c. what is its volume at the final temperature?

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Explanation:

Step1: Identify the gas law

This problem involves the volume and temperature of a gas, so we use Charles's Law, which states that for a fixed amount of gas at constant pressure, $\frac{V_1}{T_1} = \frac{V_2}{T_2}$, where $V_1$ and $T_1$ are the initial volume and temperature, and $V_2$ and $T_2$ are the final volume and temperature. Temperatures must be in Kelvin.

Step2: Convert temperatures to Kelvin

Initial temperature $T_1 = 22^\circ\text{C} + 273.15 = 295.15\,\text{K}$
Final temperature $T_2 = 87^\circ\text{C} + 273.15 = 360.15\,\text{K}$
Initial volume $V_1 = 48.3\,\text{mL}$

Step3: Solve for $V_2$

Rearrange Charles's Law: $V_2 = V_1 \times \frac{T_2}{T_1}$
Substitute values: $V_2 = 48.3\,\text{mL} \times \frac{360.15\,\text{K}}{295.15\,\text{K}}$

Step4: Calculate the value

First, calculate the ratio $\frac{360.15}{295.15} \approx 1.220$
Then, $V_2 \approx 48.3\,\text{mL} \times 1.220 \approx 58.9\,\text{mL}$ (rounded appropriately)

Answer:

The final volume of the gas is approximately $\boldsymbol{58.9\,\text{mL}}$ (or more precisely, using exact calculation: $48.3 \times \frac{360.15}{295.15} \approx 58.9\,\text{mL}$)