An Unknown gas effuses at a rate that is 0.355 times the rate of oxygen gas effuses at the same
temperature, calculate the density of this gas knowing that density of oxygen is 1.429 grams per liter.
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To calculate the density of the unknown gas, we need to use Graham's law of effusion.
According to Graham's law of effusion, the ratio of the effusion rate of two gases is equal to the square root of the inverse ratio of their molar masses.
In this case, we are comparing the effusion rate of the unknown gas to that of oxygen gas. Let's assume the molar mass of the unknown gas is M.
The effusion rate ratio is given as 0.355, which means the ratio of the unknown gas effusion rate to the oxygen gas effusion rate is 0.355.
Using Graham's law of effusion, we have:
(M unknown gas / M oxygen gas) = √(rate oxygen gas / rate unknown gas)
Substituting in the given values and simplifying:
(M / 32 g/mol) = √(1 / 0.355)
(M / 32) = √(2.819)
Taking the square of both sides:
M / 32 = 1.677
Multiplying both sides by 32:
M = 53.664 g/mol
The molar mass of the unknown gas is approximately 53.664 g/mol.
Next, we can calculate the density using the molar mass and the given density of oxygen.
Density = molar mass / molar volume
Given that the density of oxygen is 1.429 g/L, we can substitute the values:
Density = 53.664 g/mol / 1.429 g/L
Density ≈ 37.565 g/L
Therefore, the density of the unknown gas is approximately 37.565 grams per liter.
To calculate the density of the unknown gas, we need to use Graham's law of effusion, which states that the rates of effusion of two gases are inversely proportional to the square roots of their molar masses.
The molar mass of a gas is equal to the product of its density and the molar volume of the gas. The molar volume of a gas at standard temperature and pressure (STP) is 22.4 liters/mol.
Let's denote the molar mass of the unknown gas as M and the molar mass of oxygen gas as MO2.
From the given information, we know that the rate of effusion of the unknown gas is 0.355 times the rate of oxygen gas effusion. Mathematically, we can express this as:
Rate_unknown = 0.355 * Rate_oxygen
Using the relationship between the rates of effusion and the molar masses, we can write:
Rate_unknown = √(MO2 / M)
Rate_oxygen = √(M / MO2)
Substituting the given values, we have:
0.355 * √(M / MO2) = √(MO2 / M)
We can simplify this equation by squaring both sides:
(0.355 * √(M / MO2))^2 = (√(MO2 / M))^2
0.355^2 * M / MO2 = MO2 / M
Now, let's solve for M:
0.355^2 * M^2 = MO2^2
M^2 = (MO2^2) / (0.355^2)
Taking the square root of both sides:
M = √((MO2^2) / (0.355^2))
Now, we can substitute the given density of oxygen gas (1.429 grams per liter) to determine MO2:
MO2 = density * molar volume = 1.429 g/L * 22.4 L/mol
Calculate MO2 using this value.
Finally, substitute MO2 and the given value for the rate of effusion of the unknown gas into the equation for M and calculate its value.
Once you have calculated the value of M (molar mass of the unknown gas), you can calculate its density using the following equation:
Density_unknown = M * (1 / molar volume)
Substitute the value of M and molar volume to find the density of the unknown gas.