A volume of 2.0 L of He at 46 degrees celsius and 1.2 atm of pressure was added to a vessel that contained 4.5 L of N2 at STP. What is the total pressure and partial pressure of each gas at STP after the He is added?
I would use (P1V1/T1) = (P2V2/T2) where P2V2 and T2 are standard conditions. Solve for He pressure at the P2, V2, and T2 conditions. That will give you partial pressure He.
Isn't the partial pressure of N2 just 1 atm or 760 torr?
To find the total pressure and partial pressure of each gas at STP after the He is added, we'll start by calculating the number of moles of He and N2 using the ideal gas law equation:
PV = nRT
For the initial conditions of He:
V_He = 2.0 L
T_He = 46 degrees Celsius = 46 + 273 = 319 K
P_He = 1.2 atm
Rearranging the equation, we have:
n_He = (P_He * V_He) / (R * T_He)
Next, let's calculate the number of moles of N2:
V_N2 = 4.5 L
T_N2 = 273 K (STP: Standard Temperature and Pressure)
P_N2 = 1 atm (STP)
n_N2 = (P_N2 * V_N2) / (R * T_N2)
Now we can find the total number of moles:
n_total = n_He + n_N2
Using Dalton's law of partial pressures, we can determine the partial pressure of each gas at STP:
P_He_STP = (n_He / n_total) * P_total
P_N2_STP = (n_N2 / n_total) * P_total
Where P_total is the total pressure of the mixture, which is equal to P_N2 (at STP) since N2 is already at STP.
Let's plug in the values and calculate the results step by step:
To find the total pressure and partial pressure of each gas after the He is added, we'll first need to calculate the number of moles of each gas.
Let's start with the He gas. We can use the ideal gas law equation, PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant (0.0821 L·atm/mol·K), and T is the temperature in Kelvin.
First, we need to convert the temperature from degrees Celsius to Kelvin. The formula to convert Celsius to Kelvin is K = °C + 273.15.
So, the temperature of 46 degrees Celsius in Kelvin is:
T(He) = 46 + 273.15 = 319.15 K
Using the ideal gas law, we can rearrange the equation to solve for the number of moles (n):
n(He) = PV(He) / RT(He)
Substituting the given values:
P(He) = 1.2 atm (the pressure of He gas)
V(He) = 2.0 L (the volume of He gas)
R = 0.0821 L·atm/mol·K (the ideal gas constant)
T(He) = 319.15 K (the temperature of He gas in Kelvin)
n(He) = (1.2 atm * 2.0 L) / (0.0821 L·atm/mol·K * 319.15 K)
n(He) ≈ 0.0935 mol (rounded to four decimal places)
Now, let's calculate the number of moles of N2 gas. Since the gases are at STP (Standard Temperature and Pressure), we know that 1 mole of any ideal gas occupies 22.4 liters at STP.
Given that the volume of N2 is 4.5 L, we can calculate the number of moles of N2:
n(N2) = V(N2) / 22.4
Substituting the given value:
V(N2) = 4.5 L (the volume of N2 gas)
n(N2) = 4.5 L / 22.4 L/mol
n(N2) ≈ 0.2018 mol (rounded to four decimal places)
Now that we have the number of moles for each gas, we can calculate the total moles and the partial pressures at STP.
Total moles = n(He) + n(N2)
Total moles ≈ 0.0935 mol + 0.2018 mol
Total moles ≈ 0.2953 mol (rounded to four decimal places)
To find the partial pressures, we'll use the equation P = (n/V) * (R * T), where P is the pressure, n is the number of moles, V is the volume, R is the ideal gas constant, and T is the temperature in Kelvin.
Using this equation, we can calculate the partial pressure of each gas at STP:
Partial pressure of He (P(He)) = (n(He) / V(Total)) * (R * T(STP))
Partial pressure of He (P(He)) = (0.0935 mol / 6.5 L) * (0.0821 L·atm/mol·K * 273.15 K)
Partial pressure of He (P(He)) ≈ 0.0125 atm (rounded to four decimal places)
Partial pressure of N2 (P(N2)) = (n(N2) / V(Total)) * (R * T(STP))
Partial pressure of N2 (P(N2)) = (0.2018 mol / 6.5 L) * (0.0821 L·atm/mol·K * 273.15 K)
Partial pressure of N2 (P(N2)) ≈ 0.5053 atm (rounded to four decimal places)
Finally, the total pressure (P(Total)) is simply the sum of the partial pressures of each gas:
P(Total) = P(He) + P(N2)
P(Total) ≈ 0.0125 atm + 0.5053 atm
P(Total) ≈ 0.5178 atm (rounded to four decimal places)
Therefore, after the He gas is added, the total pressure is approximately 0.5178 atm, and the partial pressures are approximately 0.0125 atm for He and 0.5053 atm for N2, all at STP.