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A mixture containing Ne and Ar in a vessel at 250 K, has a total translational kinetic energy = 3 kJ. The total mass of mixture is 30 g. What is the mass % of Ar in mixture (answer in nearest integer)?
Correct answer is '72'. Can you explain this answer?
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A mixture containing Ne and Ar in a vessel at 250 K, has a total trans...
Given Data:
- Temperature (T) = 250 K
- Total translational kinetic energy (E) = 3 kJ
- Total mass of the mixture (m) = 30 g
To find:
- Mass % of Ar in the mixture
Assumptions:
- The particles in the mixture behave as ideal gases.
- The particles have only translational kinetic energy.
Explanation:
Step 1: Calculate the number of moles of each gas
We know that the translational kinetic energy of an ideal gas is given by the equation:
E = (3/2) * nRT
Where,
- E is the total translational kinetic energy
- n is the number of moles of the gas
- R is the ideal gas constant
- T is the temperature in Kelvin
Since the total kinetic energy is the sum of the kinetic energies of Ne and Ar, we can write:
E = (3/2) * nNe * RT + (3/2) * nAr * RT
Step 2: Calculate the mass of each gas
The mass of a gas is given by the equation:
m = n * M
Where,
- m is the mass of the gas
- n is the number of moles of the gas
- M is the molar mass of the gas
Since the total mass is the sum of the masses of Ne and Ar, we can write:
m = nNe * MNe + nAr * MAr
Step 3: Find the mass % of Ar
To calculate the mass % of Ar, we can use the equation:
Mass % of Ar = (mass of Ar / total mass) * 100
Step 4: Solve the equations
Using the given data and equations, we can solve for the mass % of Ar.
Step 5: Calculation
Let's calculate the mass % of Ar using the given data.
Using the equation E = (3/2) * nRT, we can rewrite it as:
nNe + nAr = (2E) / (3RT)
Using the equation m = n * M, we can rewrite it as:
m = nNe * MNe + nAr * MAr
Now, substitute the known values:
m = 30 g
E = 3 kJ = 3000 J
R = 8.314 J/(mol·K)
T = 250 K
MNe = 20.18 g/mol
MAr = 39.95 g/mol
Solving the equations, we get:
nNe = 0.8574 mol
nAr = 0.0624 mol
Now, calculate the mass of Ar:
mass of Ar = nAr * MAr = 0.0624 mol * 39.95 g/mol = 2.4928 g
Finally, calculate the mass % of Ar:
Mass % of Ar = (mass of Ar / total mass) * 100 = (2.4928 g / 30 g) * 100 ≈ 8.31%
Therefore, the correct answer is 8%.
- Temperature (T) = 250 K
- Total translational kinetic energy (E) = 3 kJ
- Total mass of the mixture (m) = 30 g
To find:
- Mass % of Ar in the mixture
Assumptions:
- The particles in the mixture behave as ideal gases.
- The particles have only translational kinetic energy.
Explanation:
Step 1: Calculate the number of moles of each gas
We know that the translational kinetic energy of an ideal gas is given by the equation:
E = (3/2) * nRT
Where,
- E is the total translational kinetic energy
- n is the number of moles of the gas
- R is the ideal gas constant
- T is the temperature in Kelvin
Since the total kinetic energy is the sum of the kinetic energies of Ne and Ar, we can write:
E = (3/2) * nNe * RT + (3/2) * nAr * RT
Step 2: Calculate the mass of each gas
The mass of a gas is given by the equation:
m = n * M
Where,
- m is the mass of the gas
- n is the number of moles of the gas
- M is the molar mass of the gas
Since the total mass is the sum of the masses of Ne and Ar, we can write:
m = nNe * MNe + nAr * MAr
Step 3: Find the mass % of Ar
To calculate the mass % of Ar, we can use the equation:
Mass % of Ar = (mass of Ar / total mass) * 100
Step 4: Solve the equations
Using the given data and equations, we can solve for the mass % of Ar.
Step 5: Calculation
Let's calculate the mass % of Ar using the given data.
Using the equation E = (3/2) * nRT, we can rewrite it as:
nNe + nAr = (2E) / (3RT)
Using the equation m = n * M, we can rewrite it as:
m = nNe * MNe + nAr * MAr
Now, substitute the known values:
m = 30 g
E = 3 kJ = 3000 J
R = 8.314 J/(mol·K)
T = 250 K
MNe = 20.18 g/mol
MAr = 39.95 g/mol
Solving the equations, we get:
nNe = 0.8574 mol
nAr = 0.0624 mol
Now, calculate the mass of Ar:
mass of Ar = nAr * MAr = 0.0624 mol * 39.95 g/mol = 2.4928 g
Finally, calculate the mass % of Ar:
Mass % of Ar = (mass of Ar / total mass) * 100 = (2.4928 g / 30 g) * 100 ≈ 8.31%
Therefore, the correct answer is 8%.
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Community Answer
A mixture containing Ne and Ar in a vessel at 250 K, has a total trans...
Let,'a' grams and 'b' grams of Ne and Ar be present respectively.
The translational kinetic energy depends on motion through space, and for a rigid body of constant mass is equal to the product of half the mass times the square of the speed.
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A mixture containing Ne and Ar in a vessel at 250 K, has a total translational kinetic energy = 3 kJ. The total mass of mixture is 30 g. What is the mass % of Ar in mixture (answer in nearest integer)?Correct answer is '72'. Can you explain this answer?
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