Question

What would the final pressure of a gas be if it had an initial and pressure of 3L and 700kPa? assume the final volume of the gas to be 5.5 L.

Answer 1

To find the final pressure of a gas given its initial pressure and volume, you can use Boyle's Law, which states that for a given amount of gas at constant temperature, the pressure of the gas is inversely proportional to its volume. The relationship can be expressed as:

\[
P_1 V_1 = P_2 V_2
\]

Where:
- \(P_1\) is the initial pressure,
- \(V_1\) is the initial volume,
- \(P_2\) is the final pressure, and
- \(V_2\) is the final volume.

Given:
- \(P_1 = 700 \, \text{kPa}\)
- \(V_1 = 3 \, \text{L}\)
- \(V_2 = 5.5 \, \text{L}\)

We need to find \(P_2\). Rearranging the equation to solve for \(P_2\):

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

Now plug in the values:

\[
P_2 = \frac{700 \, \text{kPa} \times 3 \, \text{L}}{5.5 \, \text{L}}
\]

Calculating the numerator:

\[
700 \, \text{kPa} \times 3 \, \text{L} = 2100 \, \text{kPa} \cdot \text{L}
\]

Now divide by the final volume:

\[
P_2 = \frac{2100 \, \text{kPa} \cdot \text{L}}{5.5 \, \text{L}} \approx 381.82 \, \text{kPa}
\]

Therefore, the final pressure \(P_2\) is approximately **381.82 kPa**.