we have 159ml of CO2 at 38.9 C and 92.4 kPa. if the conditions change to 64.9 C and 174 kPa, what is the volume of the gas?
Use (P1V1/T1)= (P2V2/T2)
Don't forget to change T to Kelvin.
To answer this question, you can use the ideal gas law equation, which states:
PV = nRT
Where:
P = pressure of the gas
V = volume of the gas
n = number of moles of gas
R = ideal gas constant
T = temperature of the gas in Kelvin
To calculate the volume of the gas, we need to find the number of moles of CO2 and convert the temperatures to Kelvin.
Step 1: Convert initial temperature to Kelvin.
To convert Celsius to Kelvin, use the following equation:
T(K) = T(C) + 273.15
Initial temperature (T1) = 38.9°C = 38.9 + 273.15 = 312.05 K
Step 2: Convert final temperature to Kelvin.
Final temperature (T2) = 64.9°C = 64.9 + 273.15 = 338.05 K
Step 3: Convert initial pressure to atmospheres.
The given pressure is in kilopascals (kPa). To convert kPa to atmospheres, use the following equation:
1 atm = 101.3 kPa
Initial pressure (P1) = 92.4 kPa = 92.4 / 101.3 = 0.912 atm
Step 4: Convert final pressure to atmospheres.
Final pressure (P2) = 174 kPa = 174 / 101.3 = 1.717 atm
Step 5: Calculate the number of moles of CO2 using the ideal gas law equation.
The ideal gas law equation can be rearranged as:
n = PV / RT
For the initial conditions:
n1 = (P1 * V1) / (R * T1)
For the final conditions:
n2 = (P2 * V2) / (R * T2)
Step 6: Calculate the volume of the gas using the ideal gas law equation.
Rearrange the equation as:
V = (n * R * T) / P
For the final conditions:
V2 = (n2 * R * T2) / P2
Now let's plug in the values to find the final volume.
R = 0.0821 atm L / (mol K) (Ideal gas constant)
T2 = 338.05 K (Final temperature)
P2 = 1.717 atm (Final pressure)
n2 = (P1 * V1) / (R * T1) (Number of moles of CO2, calculated using initial conditions)
Calculate n2 as follows:
n2 = (0.912 * 159 mL) / (0.0821 * 312.05) mol
n2 ≈ 6.048 mol
Now calculate the final volume (V2):
V2 = (6.048 mol * 0.0821 atm L / (mol K) * 338.05 K) / 1.717 atm
V2 ≈ 76.65 L
Therefore, the volume of the gas at the new conditions (64.9°C and 174 kPa) is approximately 76.65 liters.