At 0*C a 1.0-L flask contains 5.0 x 10^-2 mol N2, 1.5 x 10^2 mg O2, and 5.0 x 10^21 molecules of NH3. What is the partial pressure of each gas, and what is the total pressure in the flask?
mols N2 = 5E-2.
mol O2 = 0.15/molar mass = ?
mol NH3 = 5.0E21/6.02E23 = ?
Use PV = nRT and mols of each to find partial pressure of each gas. Add partial pressures to find total pressure.
To find the partial pressure of each gas and the total pressure in the flask, we need to use the ideal gas law equation, which is:
PV = nRT
Where:
P = pressure in atmospheres (atm)
V = volume in liters (L)
n = number of moles (mol)
R = ideal gas constant, which is 0.0821 L atm/(mol K)
T = temperature in Kelvin (K)
First, let's calculate the total number of moles of each gas:
1. For N2:
Given: 5.0 x 10^-2 mol N2
2. For O2:
Given: 1.5 x 10^2 mg O2
To convert milligrams (mg) to grams (g):
1 g = 1000 mg
1.5 x 10^2 mg O2 = 1.5 x 10^2 / 1000 = 0.15 g O2
To convert grams (g) to moles (mol):
Molar mass of O2 (32 g/mol)
0.15 g O2 = 0.15 / 32 = 0.0046875 mol O2
3. For NH3:
Given: 5.0 x 10^21 molecules of NH3
To convert molecules to moles, we need to know Avogadro's number:
1 mole = 6.022 x 10^23 molecules
5.0 x 10^21 NH3 molecules = 5.0 x 10^21 / 6.022 x 10^23 = 8.304 x 10^-3 mol NH3
Now, let's calculate the partial pressure of each gas:
Partial pressure (P) = (n * R * T) / V
Note: Since the temperature is given in Celsius, we need to convert it to Kelvin by adding 273.15.
Given: Temperature (T) = 0 *C = 273.15 K
Volume (V) = 1.0 L
R = 0.0821 L atm/(mol K)
1. For N2:
Partial pressure (P) = (5.0 x 10^-2 mol * 0.0821 L atm/(mol K) * 273.15 K) / 1.0 L
P(N2) = 1.209 atm
2. For O2:
Partial pressure (P) = (0.0046875 mol * 0.0821 L atm/(mol K) * 273.15 K) / 1.0 L
P(O2) = 0.100 atm
3. For NH3:
Partial pressure (P) = (8.304 x 10^-3 mol * 0.0821 L atm/(mol K) * 273.15 K) / 1.0 L
P(NH3) = 0.184 atm
Finally, to calculate the total pressure in the flask, we add up the partial pressures of all the gases:
Total pressure = P(N2) + P(O2) + P(NH3)
Total pressure = 1.209 atm + 0.100 atm + 0.184 atm
Total pressure = 1.493 atm
Therefore, the partial pressures of each gas are:
P(N2) = 1.209 atm
P(O2) = 0.100 atm
P(NH3) = 0.184 atm
And the total pressure in the flask is 1.493 atm.