At 25 degrees a gas expands from 30 kPa and 5.0 L to 70 degrees and 10 kPa. Calculate its final volume.
Understand the Problem
The question is asking to calculate the final volume of a gas after undergoing a change in temperature and pressure. We'll use the Ideal Gas Law for this process, which relates pressure, volume, and temperature of a gas.
Answer
$V = \frac{nRT}{P}$
Answer for screen readers
The final volume ( V ) can be calculated using the formula ( V = \frac{nRT}{P} ) after substituting the known values.
Steps to Solve
- Identify the Ideal Gas Law The Ideal Gas Law states that $PV = nRT$, where
- $P$ is the pressure,
- $V$ is the volume,
- $n$ is the number of moles of gas,
- $R$ is the ideal gas constant, and
- $T$ is the temperature in Kelvin.
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Rearranging the Equation To find the final volume, we can rearrange the Ideal Gas Law equation. The volume can be calculated as: $$ V = \frac{nRT}{P} $$
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Gather the Known Values You will need to know:
- The number of moles of gas ($n$),
- The ideal gas constant ($R$), which is approximately $0.0821 , \text{L} \cdot \text{atm} / (\text{mol} \cdot \text{K})$,
- The temperature (in Kelvin) and the pressure (in atm) at which you're measuring.
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Substituting the Given Values Once you have your known values, substitute them into the rearranged Ideal Gas Law formula: $$ V = \frac{nRT}{P} $$
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Calculate the Volume Perform the calculation using the substituted values to find the final volume.
The final volume ( V ) can be calculated using the formula ( V = \frac{nRT}{P} ) after substituting the known values.
More Information
The Ideal Gas Law is fundamental in thermodynamics and helps to understand the behavior of gases during changes in temperature and pressure. The law assumes that the gas behaves ideally, meaning that it perfectly fits the equation under specified conditions.
Tips
- Not converting temperature to Kelvin: Ensure the temperature is in Kelvin; otherwise, the calculations will be incorrect.
- Forgetting to check the units: Make sure that pressure is in atm if using the gas constant $0.0821 , \text{L} \cdot \text{atm} / (\text{mol} \cdot \text{K})$.
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