At 0 degrees celcius, a 1.0 L flask contains 5.0 x 10^-2 mol N2, 1.5 x 10^2 mg O2, 5.0 x 10^21 molecules NH3. Calculate the partial pressure of each gas and what is the total pressure in the flask.
How do I calculate this?
Convert gases to mols.
You have mols N2.
mols O2 = grams/molar mass.
mols NH3 = # molecules/6.02E23
Plug each gas into PV = nRT (n = mols) and solve for the partial pressure of each gas. The total P is the sum of the partial pressures.
Well, let's see here. To calculate the partial pressure of each gas, you'll need to use the ideal gas law equation, which is: PV = nRT. Let's break it down step by step.
Step 1: Convert the mass of O2 into moles.
Given: 1.5 x 10^2 mg O2
To convert milligrams to grams: 1 mg = 1 x 10^-3 g
So, 1.5 x 10^2 mg O2 = 1.5 x 10^2 x 10^-3 g = 0.15 g O2
Given: Assumed molar mass of O2 = 32 g/mol
Now to convert grams to moles:
0.15 g O2 x (1 mol O2 / 32 g O2) = 0.0046875 mol O2
Step 2: Calculate the amount of NH3 in moles.
Given: 5.0 x 10^21 molecules NH3
We know that 1 mole of any substance contains 6.022 x 10^23 particles (Avogadro's number).
So, the number of moles of NH3 is calculated as follows:
5.0 x 10^21 molecules NH3 x (1 mol NH3 / 6.022 x 10^23 molecules NH3) ≈ 8.29 x 10^-3 mol NH3
Step 3: Calculate the partial pressure for each gas.
Remember, the ideal gas law is PV = nRT, so we need to rearrange it to solve for pressure (P):
P = nRT / V
Given: Volume (V) = 1.0 L
Given: Temperature (T) = 0 degrees Celsius (convert to Kelvin: 0 + 273.15 = 273.15 K)
Given: R = 0.0821 L·atm/(mol·K) (gas constant)
For N2:
P(N2) = (5.0 x 10^-2 mol N2 x 0.0821 L·atm/(mol·K) x 273.15 K) / 1.0 L = 1.14 atm
For O2:
P(O2) = (0.0046875 mol O2 x 0.0821 L·atm/(mol·K) x 273.15 K) / 1.0 L = 0.10 atm (approximately)
For NH3:
P(NH3) = (8.29 x 10^-3 mol NH3 x 0.0821 L·atm/(mol·K) x 273.15 K) / 1.0 L = 1.69 x 10^-1 atm
Step 4: Calculate the total pressure in the flask.
Total pressure = P(N2) + P(O2) + P(NH3)
= 1.14 atm + 0.10 atm + 1.69 x 10^-1 atm
= 2.41 atm
So, the partial pressure of N2, O2, and NH3 is approximately 1.14 atm, 0.10 atm, and 1.69 x 10^-1 atm, respectively. And the total pressure in the flask is approximately 2.41 atm.
To calculate the partial pressure of each gas and the total pressure in the flask, you need to use the ideal gas law and the concept of moles.
1. Convert the given values to SI units (moles for all substances).
a. Convert the mass of O2 from milligrams to grams: 1.5 x 10^2 mg = 0.15 g.
b. Convert the number of molecules of NH3 to moles: 5.0 x 10^21 molecules NH3.
2. Determine the number of moles for each gas using their molar masses:
a. N2 (nitrogen gas): The molar mass of N2 is approximately 28.01 g/mol, so the number of moles is 5.0 x 10^-2 mol.
b. O2 (oxygen gas): The molar mass of O2 is approximately 32.00 g/mol, so the number of moles is given by the mass divided by the molar mass: 0.15 g / 32.00 g/mol.
c. NH3 (ammonia gas): The molar mass of NH3 is approximately 17.03 g/mol, so the number of moles is given by the molecules divided by Avogadro's number: 5.0 x 10^21 molecules NH3 / 6.022 x 10^23 molecules/mol.
3. Use the ideal gas law (PV = nRT) to calculate the partial pressures:
a. Since the temperature is given as 0 degrees Celsius, convert it to Kelvin: 0°C + 273.15 = 273.15 K.
b. Rearrange the ideal gas law to solve for pressure (P = nRT/V) and substitute the values:
- For N2: P_N2 = (n_N2 * R * T) / V
- For O2: P_O2 = (n_O2 * R * T) / V
- For NH3: P_NH3 = (n_NH3 * R * T) / V
4. Calculate the total pressure by summing the partial pressures:
Total pressure = P_N2 + P_O2 + P_NH3
Note: In these calculations, R is the ideal gas constant (approximately 0.0821 L·atm/(mol·K)) and V is the volume of the flask (1.0 L).
Perform these calculations to determine the partial pressure of each gas and the total pressure in the flask.
To calculate the partial pressure of each gas and the total pressure in the flask, you need to apply the ideal gas law equation. The ideal gas law is represented by the equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
Before we begin, we need to convert the given quantities to the appropriate units:
- The temperature is given as 0 degrees Celsius, so we need to convert it to Kelvin. To do this, we add 273.15 to the Celsius temperature.
- The amount of O2 is given in milligrams, so we need to convert it to moles using the molar mass of O2 (32 g/mol).
- The amount of NH3 is given in molecules, so we need to convert it to moles. Since Avogadro's number tells us that 1 mole of any substance contains 6.022 x 10^23 particles, we can divide the number of molecules by Avogadro's number to get the number of moles.
Now, let's calculate the partial pressure of each gas and the total pressure step by step:
1. Calculate the number of moles of N2:
n(N2) = 5.0 x 10^-2 mol
2. Calculate the number of moles of O2:
n(O2) = (1.5 x 10^2 mg / 32 g/mol) = 4.6875 x 10^-3 mol
3. Calculate the number of moles of NH3:
n(NH3) = (5.0 x 10^21 molecules) / (6.022 x 10^23 molecules/mol) = 8.305 x 10^-3 mol
4. Calculate the total number of moles:
n(total) = n(N2) + n(O2) + n(NH3)
5. Convert the temperature to Kelvin: T = 0°C + 273.15 = 273.15 K
6. Identify the volume given as 1.0 L.
7. Use the ideal gas law equation to calculate the partial pressure of each gas:
- For N2: P(N2) = (n(N2) * R * T) / V
- For O2: P(O2) = (n(O2) * R * T) / V
- For NH3: P(NH3) = (n(NH3) * R * T) / V
8. Calculate the total pressure by summing up the partial pressures: P(total) = P(N2) + P(O2) + P(NH3).
Remember to use the appropriate gas constant (R) based on the units used. For example, if you are using pressure in atm, volume in liters, and temperature in Kelvin, the value of R would be 0.0821 L·atm/(mol·K).
By following these steps and plugging in the calculated values, you should be able to find the partial pressure of each gas and the total pressure in the flask.