A gaseous mixture of O2, H2, and N2 has a total pressure of 1.50 atm and contains 8.20 g
of each gas. Find the partial pressure of each gas in the mixture
They don't give you Volume and Temperature. Please explain it to me, thank you!
You want to convert 8.2 g O2 to moles, 8.2 g N2 to moles, 8.2 g H2 to moles.
Then determine the mole fraction of each.
partial pressure each = Xof each*1.5 atm.
moles fraction, O2 for example, = moles O2/total number of moles.
Ah, the gaseous mixture! A classic tale of gases coming together. Now, let's dive into your question.
To find the partial pressure of each gas, we can use Dalton's Law of Partial Pressures. According to this law, the total pressure of a mixture of non-reacting gases is the sum of the partial pressures of the individual gases.
First, we need to find the number of moles for each gas. To do this, we can use the ideal gas law equation: PV = nRT.
However, as you mentioned, we don't have the volume and temperature. But fear not! There's a trick we can use. Since the volume and temperature is the same for all gases in the mixture, we can assume they cancel each other out in the calculations. So, let's proceed.
The equation PV = nRT can be rearranged to n = PV/RT, where n is the number of moles. Since we have the same mass for each gas, we can assume they have the same volume. Hence, their partial pressures will be proportional to their number of moles.
Now, let's calculate the moles of each gas using the mass and molar mass.
For oxygen (O2):
Molar Mass of O2 = 32 g/mol
Moles of O2 = 8.20 g / 32 g/mol
For hydrogen (H2):
Molar Mass of H2 = 2 g/mol
Moles of H2 = 8.20 g / 2 g/mol
For nitrogen (N2):
Molar Mass of N2 = 28 g/mol
Moles of N2 = 8.20 g / 28 g/mol
Now that we have the moles for each gas, we can find the partial pressure. Remember, the partial pressure is proportional to the number of moles:
Partial Pressure of O2 = (moles of O2 / Total moles) * Total pressure
Partial Pressure of H2 = (moles of H2 / Total moles) * Total pressure
Partial Pressure of N2 = (moles of N2 / Total moles) * Total pressure
Plug in the values and let the calculations commence!
I hope that explanation didn't blow too much hot air. Now go forth and conquer those partial pressures!
To find the partial pressure of each gas in the mixture, we can use the concept of mole fraction.
First, we need to find the number of moles of each gas present in the mixture. We can use the ideal gas 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. Since the volume and temperature are not given, we can assume they are constant and cancel them out in the equation.
Considering the ideal gas equation, we can rewrite it as P = nRT/V. Since we are concerned with the partial pressures, we can rewrite the equation further as P_i = n_iRT/V, where P_i is the partial pressure of gas i and n_i is the number of moles of gas i.
To find the number of moles of each gas (n_i), we need to use the given mass of each gas and their molar masses. The molar mass of oxygen (O2) is 32 g/mol, hydrogen (H2) is 2 g/mol, and nitrogen (N2) is 28 g/mol. Using these values, we can calculate the number of moles of each gas.
Number of moles (n) = mass (m) / molar mass (M)
For oxygen (O2):
n_O2 = 8.20 g / 32 g/mol = 0.25625 mol
For hydrogen (H2):
n_H2 = 8.20 g / 2 g/mol = 4.10 mol
For nitrogen (N2):
n_N2 = 8.20 g / 28 g/mol = 0.29286 mol
Next, we need to calculate the total number of moles for the mixture:
n_total = n_O2 + n_H2 + n_N2 = 0.25625 mol + 4.10 mol + 0.29286 mol = 4.6491 mol
Now, we can calculate the mole fractions for each gas as follows:
Mole fraction (X) = n_i / n_total
For oxygen (O2):
X_O2 = 0.25625 mol / 4.6491 mol = 0.055135
For hydrogen (H2):
X_H2 = 4.10 mol / 4.6491 mol = 0.882173
For nitrogen (N2):
X_N2 = 0.29286 mol / 4.6491 mol = 0.062692
Finally, we can calculate the partial pressure of each gas using the mole fractions and total pressure:
Partial pressure (P_i) = X_i * P_total
For oxygen (O2):
P_O2 = 0.055135 * 1.50 atm = 0.0827 atm
For hydrogen (H2):
P_H2 = 0.882173 * 1.50 atm = 1.3233 atm
For nitrogen (N2):
P_N2 = 0.062692 * 1.50 atm = 0.0940 atm
So the partial pressures of oxygen (O2), hydrogen (H2), and nitrogen (N2) in the mixture are approximately 0.0827 atm, 1.3233 atm, and 0.0940 atm, respectively.
To find the partial pressure of each gas in the mixture, you can use the idea of the mole fraction. The mole fraction is a ratio that represents the relative amount of a component in a mixture.
Here's how you can calculate the partial pressure of each gas:
1. Determine the number of moles for each gas:
- To find the number of moles, divide the mass of each gas by its respective molar mass. For O2, H2, and N2, the molar masses are approximately 32 g/mol, 2 g/mol, and 28 g/mol, respectively.
- Use the formula: Number of moles = mass / molar mass.
- For all three gases, since they all have a mass of 8.20 g, the number of moles will be the same.
2. Calculate the total moles of gas in the mixture:
- Since all three gases have the same number of moles, multiply the number of moles by three to get the total moles in the mixture.
3. Find the mole fraction for each gas:
- Mole fraction is calculated by dividing the number of moles of a specific gas by the total moles in the mixture.
- For each gas, divide the number of moles of that gas by the total moles in the mixture.
4. Calculate the partial pressure of each gas:
- The partial pressure of each gas is equal to its mole fraction multiplied by the total pressure of the mixture.
- Multiply the mole fraction for each gas by the total pressure of 1.50 atm to obtain the partial pressure.
Since the given question does not provide information regarding volume and temperature, the calculation of partial pressures does not require these variables.