A sample of gas exerts a pressure of 8.2atm when continued in a 2.93dm3 container at 20% the number of more of the sample is (R =0.082 atm/dm3 k1 mol1
To solve this problem, we'll need to use the ideal gas law:
PV = nRT
where P is the pressure of the gas, V is the volume of the container, n is the number of moles of the gas, R is the gas constant, and T is the temperature of the gas in Kelvin.
We're given P, V, and R, so we can solve for n:
n = PV/RT
To find T, we need to use the percent composition of the gas. Let's assume that the gas is made up of 20% of some molecule X, and 80% of some other molecule Y. Then the total number of moles in the gas will be:
n_total = n_X + n_Y
We don't know the individual quantities of n_X and n_Y, but we do know that the mole fraction of X is 0.2. This means that:
n_X/n_total = 0.2
We can rearrange this equation to solve for n_X:
n_X = 0.2n_total
Now we can substitute this expression for n_X into our original equation:
n_total = n_X + n_Y
n_total = 0.2n_total + n_Y
0.8n_total = n_Y
n_Y = 0.8n_total
So the mole fraction of Y is 0.8. We can use the mole fractions to calculate the partial pressures of X and Y:
P_X = 0.2P_total
P_Y = 0.8P_total
Now let's substitute these equations into the ideal gas law:
PV_total = n_totalRT
(P_XV + P_YV) = n_totalRT
(0.2P_totalV + 0.8P_totalV) = n_totalRT
P_totalV = n_totalRT
Now we can solve for n_total:
n_total = P_totalV/RT
n_total = (8.2 atm)(2.93 dm^3)/(0.082 atm/dm^3K mol)(293 K)
n_total = 0.979 mol
Since we know that the mole fraction of X is 0.2, we can calculate the number of moles of X:
n_X = 0.2n_total
n_X = 0.196 mol
Therefore, the number of moles of the gas that is made up of molecule X is 0.196 mol.
To find the number of moles of the gas sample, we can use the Ideal Gas Law:
PV = nRT
Where:
P = pressure of the gas (in atm)
V = volume of the gas (in dm^3)
n = number of moles of gas
R = ideal gas constant (0.082 atm•dm^3/K•mol)
T = temperature of the gas (in Kelvin)
Given:
P = 8.2 atm
V = 2.93 dm^3
R = 0.082 atm•dm^3/K•mol
We need to convert the given temperature to Kelvin. The Kelvin scale is obtained by adding 273.15 to the temperature in Celsius. If the temperature is not given, we need to assume a value.
Let's assume a temperature of 25 degrees Celsius (which is equal to 298 Kelvin).
Substituting the values into the equation:
8.2 * 2.93 = n * 0.082 * 298
Multiply the left side of the equation:
23.946 = n * 24.436
Divide both sides by 24.436 to isolate n:
n = 23.946 / 24.436
n ≈ 0.979 mol
Therefore, the number of moles of the gas sample is approximately 0.979 moles.