a closed gas cylinder contains 0.500 mole h2, 0.300 mole o2, 1.200 mole co2 at a temperature of 25'c and presure of 2.00 atm
1) calculate the volume of the cylinder
2) calculatethe partial pressure of the cylinder if the volime is decreased to 25% of its original value at consistant tempurature
To solve both parts of the question, we need to use the Ideal Gas Law, which states:
PV = nRT
where:
P = Pressure of the gas
V = Volume of the gas
n = number of moles of the gas
R = Ideal Gas Constant (0.0821 L·atm/(K·mol))
T = temperature in Kelvin
Let's solve the two parts of the question step by step:
1) To calculate the volume of the cylinder, we can rearrange the Ideal Gas Law equation to solve for V:
V = (nRT) / P
Given:
n(H2) = 0.500 moles
n(O2) = 0.300 moles
n(CO2) = 1.200 moles
T = 25 °C = 25 + 273.15 = 298.15 K
P = 2.00 atm
First, let's calculate the total number of moles:
n(total) = n(H2) + n(O2) + n(CO2)
n(total) = 0.500 + 0.300 + 1.200
n(total) = 2.000 moles
Now, substitute the values into the equation:
V = (n(total) * R * T) / P
V = (2.000 * 0.0821 * 298.15) / 2.00
V = 49.00775 L
V ≈ 49.0 L
Therefore, the volume of the cylinder is approximately 49.0 liters.
2) To calculate the partial pressure of the cylinder when the volume is decreased to 25% of its original value at a constant temperature, we will assume that the moles of gas remain constant.
Given:
Initial volume (V1) = 49.0 L
Final volume (V2) = 25% of V1 = 0.25 * 49.0 L = 12.25 L
n(total) = 2.000 moles
T = 298.15 K (constant)
Using the Ideal Gas Law again, we can determine the new pressure (P2):
P1 * V1 = P2 * V2
Solving for P2:
P2 = (P1 * V1) / V2
Substitute the given values:
P2 = (2.00 atm * 49.0 L) / 12.25 L
P2 ≈ 7.99 atm
Therefore, the partial pressure of the cylinder, when the volume is decreased to 25% of its original value, is approximately 7.99 atm.
1) Use PV = nRT. You have P, R, T (must be in kelvin) with total n = 0.500+0.300+1.200 = ? Solve for V in L.
2) You meant constant T I assume (instead of consistent T). Multiply V in part 1 by 0.25 and use PV = nRT again. This time V is the new number (multiplied by 0.25), solve for P in atm, n, R, and T are the same as in part 1.