300ml of gas at 27•C is cooled to -3•C at constant pressure the final ...
300ml of gas at 27•C is cooled to -3•C at constant pressure the final ...
Initial Conditions:
- Volume of gas (V1) = 300 ml
- Temperature of gas (T1) = 27°C
- Pressure of gas (P1) = Constant
Final Conditions:
- Temperature of gas (T2) = -3°C
- Pressure of gas (P2) = Constant
- Volume of gas (V2) = ?
Gas Law:
To solve this problem, we can use the ideal gas law, which relates the pressure, volume, and temperature of a gas.
Step 1: Convert temperatures to Kelvin:
To use the ideal gas law, we need to convert the temperatures from Celsius to Kelvin. The Kelvin scale is an absolute temperature scale with 0 K representing absolute zero.
- Initial temperature (T1) = 27°C = 27 + 273 = 300 K
- Final temperature (T2) = -3°C = -3 + 273 = 270 K
Step 2: Apply the ideal gas law:
The ideal gas law is given by the equation: 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.
Since the pressure is constant, we can rewrite the equation as: V1/T1 = V2/T2
Step 3: Substitute the given values:
- V1/T1 = V2/T2
- 300 ml / 300 K = V2 / 270 K
Step 4: Solve for V2:
Cross-multiply the equation and solve for V2:
- 300 ml * 270 K = V2 * 300 K
- 81000 ml * K = V2 * 300 K
Step 5: Convert units and calculate V2:
- 81000 ml * K = V2 * 300 K
- 81000 ml * K / 300 K = V2
- 270 ml = V2
Final Answer:
The final volume of the gas is 270 ml.