A mixture of N2(g) and H2(g) has mole fractions of .40 and .60, respectively. What is the density of the mixture at 1 bar and 0 degrees celsius?
To find the density of the mixture, you need to know the molar mass and the total number of moles of the mixture.
First, calculate the molar mass of the mixture using the molar masses of nitrogen (N2) and hydrogen (H2). The molar mass of N2 is 28.0134 g/mol, and the molar mass of H2 is 2.0159 g/mol.
Molar mass of the mixture = (mole fraction of N2 * molar mass of N2) + (mole fraction of H2 * molar mass of H2)
= (0.40 * 28.0134 g/mol) + (0.60 * 2.0159 g/mol)
Next, calculate the total number of moles of the mixture. Since mole fraction is the ratio of the number of moles of a component to the total number of moles, you can use the mole fractions directly as the number of moles.
Number of moles of the mixture = mole fraction of N2 + mole fraction of H2
= 0.40 + 0.60
Now you have the molar mass of the mixture and the total number of moles.
Using the ideal gas law, you can calculate the density of the mixture at a given temperature and pressure:
density = (molar mass of the mixture * pressure) / (R * temperature)
where R is the ideal gas constant, which is 0.0831 L·bar/mol·K.
Substituting the values into the equation:
density = (molar mass of the mixture * pressure) / (R * temperature)
= (molar mass of the mixture * 1 bar) / (0.0831 × 273 K)
Now, just substitute the values you calculated to find the density of the mixture at 1 bar and 0 degrees Celsius.
If you take 1 mol of the mixture,
g N2 = 0.4mol x 28 g/mol = ? g N2
g H2 = 0.6mol x 2 g/mol = ? g H2.
density = total g/22.4 L = ? g/L.