Question

What would the initial volume of a gas has been if it's final volume and temperature are 27L and 370K?
Assume the initial temperature was 410K

Answer 1

To find the initial volume of a gas given its final volume and temperatures, we can use the combined gas law, which relates the initial and final states of a gas under varying temperature and volume conditions. The combined gas law is expressed as:

\[
\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}
\]

In this expression:
- \(P_1\) and \(P_2\) are the initial and final pressures (which we will assume are constant for simplification).
- \(V_1\) is the initial volume we want to find.
- \(V_2 = 27 \, L\) is the final volume.
- \(T_1 = 410 \, K\) is the initial temperature.
- \(T_2 = 370 \, K\) is the final temperature.

Assuming the pressure remains constant, we can simplify our equation to:

\[
\frac{V_1}{T_1} = \frac{V_2}{T_2}
\]

Rearranging to solve for \(V_1\):

\[
V_1 = V_2 \cdot \frac{T_1}{T_2}
\]

Now substituting the known values:

\[
V_1 = 27 \, L \cdot \frac{410 \, K}{370 \, K}
\]

Calculating the ratio:

\[
V_1 = 27 \, L \cdot \frac{410}{370}
\]
\[
V_1 = 27 \, L \cdot 1.1081 \approx 29.92 \, L
\]

Therefore, the initial volume \(V_1\) of the gas is approximately **29.92 L**.