The volume of a sample of a gas collected over water at 32 Celsius and 752 torr is 627 ml. What will the volume of the gas be when dried and measured at STP?
(Vapor pressure of water at 32 Celsius = 35.7 torr)
(P1V1/T1) = (P2V2/T2)
P1 = 752-35.7
V1 = 627
T1 = (273 + 32)
P2, and T2 are standard conditions.
Solve for V2
A sample of oxygen, O2, occupies 32.2 mL at 30 °C and 452 torr. What volume will it occupy at –70 °C and the same pressure?
To find the volume of the gas when dried and measured at STP (Standard Temperature and Pressure), we can use the combined gas law equation. The combined gas law relates the initial and final conditions of a gas sample:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where P1 and P2 are the initial and final pressures, V1 and V2 are the initial and final volumes, and T1 and T2 are the initial and final temperatures.
Given:
P1 = 752 torr (pressure over water at 32 Celsius)
V1 = 627 ml (initial volume)
T1 = 32 Celsius (initial temperature)
P2 = ? (final pressure at STP)
V2 = ? (final volume at STP)
T2 = 0 Celsius (STP temperature, which is 273.15 Kelvin)
We also have the vapor pressure of water at 32 Celsius, which is given as 35.7 torr.
Now, let's calculate the final volume of the gas when dried and measured at STP.
Step 1: Convert the initial temperature from Celsius to Kelvin.
T1 (in Kelvin) = T1 (in Celsius) + 273.15
T1 = 32 + 273.15
T1 = 305.15 K
Step 2: Substitute the given values into the combined gas law equation.
(P1 * V1) / (T1) = (P2 * V2) / (T2)
(752 torr * 627 ml) / (305.15 K) = (P2 * V2) / (273.15 K)
Step 3: Solve for P2 (final pressure at STP).
P2 = ((752 torr * 627 ml) / (305.15 K)) * (273.15 K)
P2 = ((752 torr * 627) / 305.15) * (273.15)
Step 4: Subtract the vapor pressure of water at 32 Celsius from P2.
P2 (adjusted) = P2 - Vapor pressure of water at 32 Celsius
P2 (adjusted) = P2 - 35.7 torr
Step 5: Substitute the final pressure P2 (adjusted) and the given volume V1 into the ideal gas law equation to find the final volume V2 at STP.
(P1 * V1) / (T1) = (P2 (adjusted) * V2) / (T2)
(752 torr * 627 ml) / (305.15 K) = (P2 (adjusted) * V2) / (273.15 K)
Step 6: Solve for V2 (final volume at STP).
V2 = ((752 torr * 627 ml * 273.15 K) / (305.15 K * P2 (adjusted))
After evaluating this equation, you will find the value of V2, which will be the final volume of the gas when dried and measured at STP.