What volume will a gas occupy at 100°C and 5.0 atm if its volume at N.T.P is 10.00 L?
Understand the Problem
The question is asking to calculate the volume of a gas at a specified temperature and pressure, given its volume at normal temperature and pressure (N.T.P). We will use the Ideal Gas Law and the concept of gas laws to solve this.
Answer
The new volume is calculated using the equation \( V_2 = V_1 \cdot \frac{P_1}{P_2} \cdot \frac{T_2}{T_1} \).
Answer for screen readers
The volume of the gas at specified temperature and pressure is given by:
$$ V_2 = V_1 \cdot \frac{P_1}{P_2} \cdot \frac{T_2}{T_1} $$
Steps to Solve
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Identify known values We need to know the initial volume ( V_1 ) at normal temperature and pressure (N.T.P), temperature ( T_1 ) at N.T.P (usually 273.15 K), pressure ( P_1 ) at N.T.P (usually 1 atm), and the new temperature ( T_2 ) and pressure ( P_2 ).
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Use the Ideal Gas Law The Ideal Gas Law states that ( PV = nRT ). However, in this case, we can use the variation of the Ideal Gas Law for the same amount of gas in different states, which can be simplified to the combined gas law given by:
$$ \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} $$
- Rearrange to find the unknown volume To find the new volume ( V_2 ), rearrange the equation:
$$ V_2 = V_1 \cdot \frac{P_1}{P_2} \cdot \frac{T_2}{T_1} $$
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Substitute the values Plug in the known values of ( V_1 ), ( P_1 ), ( P_2 ), ( T_1 ), and ( T_2 ) into the equation to calculate ( V_2 ).
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Calculate the new volume Perform the calculation to find the value of ( V_2 ).
The volume of the gas at specified temperature and pressure is given by:
$$ V_2 = V_1 \cdot \frac{P_1}{P_2} \cdot \frac{T_2}{T_1} $$
More Information
The volume of gas varies with changes in pressure and temperature according to the Ideal Gas Law. It helps in understanding how gases behave under different conditions, which is crucial in fields like chemistry and engineering.
Tips
- Confusing temperature units: Always ensure temperatures are in Kelvin to avoid calculation errors.
- Ignoring the relationship between pressure and volume: Remember that if pressure increases, volume should decrease if temperature is constant, and vice versa.
- Failing to convert pressures to the same units: Always check that pressures are in the same unit before substituting into the formula.
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