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A quantity of 10 g of an ideal gas is expanded at constant temperature until it's pressure becomes half of the initial pressure.the quantity of 1.25 g of the rarefied gas occupies 50 ml at the same final pressure and temperature.The initial volume of the gas was
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A quantity of 10 g of an ideal gas is expanded at constant temperature...
Initial Conditions of the Ideal Gas
To determine the initial volume of the ideal gas, we can utilize the ideal gas law, which states that PV = nRT.
- Parameters Defined:
- P: Pressure
- V: Volume
- n: Number of moles
- R: Ideal gas constant
- T: Temperature
Expansion at Constant Temperature
- The gas expands isothermally, meaning temperature (T) remains constant.
- The pressure of the gas is reduced to half its initial value (P_initial / 2).
Relationship Between Initial and Final Volumes
- According to Boyle's Law (P1V1 = P2V2), the initial and final states are related:
- Initial volume (V_initial) and final volume (V_final) can be expressed as:
- P_initial * V_initial = (P_initial / 2) * V_final
- This simplifies to:
- V_final = 2 * V_initial
Calculating Moles of the Rarefied Gas
- For the 1.25 g of the rarefied gas:
- Given: V_final = 50 ml at final pressure (P_final) and temperature (T).
- To find the number of moles, use n = mass / molar mass.
- Assuming the molar mass of the rarefied gas is known, calculate the moles (n).
Final Calculation of Initial Volume
- From the isothermal expansion, we have V_final = 2 * V_initial.
- With the volume of the rarefied gas known, we can equate and solve for V_initial.
- If V_final (50 ml) is equal to 2 * V_initial, we can derive:
- V_initial = 50 ml / 2 = 25 ml
Thus, the initial volume of the ideal gas was 25 ml.
Community Answer
A quantity of 10 g of an ideal gas is expanded at constant temperature...
200 ml
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A quantity of 10 g of an ideal gas is expanded at constant temperature until it's pressure becomes half of the initial pressure.the quantity of 1.25 g of the rarefied gas occupies 50 ml at the same final pressure and temperature.The initial volume of the gas was
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