Вопрос школьника
Determine the volume fraction of nitrogen in the mixture thereof with ammonia , if the mass fraction of nitrogen in the mixture is 62,2 %.
Ответ от учителя
To determine the volume fraction of nitrogen in the mixture with ammonia, we need to know the density of the mixture. However, this information is not given in the question. Therefore, we cannot directly calculate the volume fraction of nitrogen in the mixture.
However, we can use the ideal gas law to estimate the volume fraction of nitrogen in the mixture. According to the ideal gas law, the volume of a gas is directly proportional to the number of moles of the gas, at constant temperature and pressure. Therefore, if we assume that the mixture behaves as an ideal gas, we can estimate the volume fraction of nitrogen in the mixture based on the number of moles of nitrogen and ammonia.
To do this, we need to convert the mass fraction of nitrogen in the mixture to the mole fraction of nitrogen in the mixture. We can use the molar masses of nitrogen and ammonia to convert the mass fraction to mole fraction:
Molar mass of nitrogen = 14.01 g/mol
Molar mass of ammonia = 17.03 g/mol
Mass fraction of nitrogen = 62.2%
Mass fraction of ammonia = 100% — 62.2% = 37.8%
Mole fraction of nitrogen = (mass fraction of nitrogen / molar mass of nitrogen) / [(mass fraction of nitrogen / molar mass of nitrogen) + (mass fraction of ammonia / molar mass of ammonia)]
= (0.622 / 14.01) / [(0.622 / 14.01) + (0.378 / 17.03)]
= 0.383
Mole fraction of ammonia = 1 — mole fraction of nitrogen
= 1 — 0.383
= 0.617
Now, we can assume that the mixture behaves as an ideal gas, and use the ideal gas law to estimate the volume fraction of nitrogen in the mixture. The ideal gas law is:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.
Assuming constant temperature and pressure, we can write:
V_nitrogen / V_total = n_nitrogen / (n_nitrogen + n_ammonia)
where V_nitrogen and V_total are the volumes of nitrogen and the mixture, respectively, and n_nitrogen and n_ammonia are the number of moles of nitrogen and ammonia, respectively.
We can rearrange this equation to solve for V_nitrogen / V_total:
V_nitrogen / V_total = n_nitrogen / (n_nitrogen + n_ammonia)
= (mole fraction of nitrogen x total number of moles) / (mole fraction of nitrogen x total number of moles + mole fraction of ammonia x total number of moles)
= mole fraction of nitrogen / (mole fraction of nitrogen + mole fraction of ammonia)
Substituting the mole fractions we calculated earlier, we get:
V_nitrogen / V_total = 0.383 / (0.383 + 0.617)
= 0.383 / 1
= 0.383
Therefore, the volume fraction of nitrogen in the mixture with ammonia is approximately 38.3%.
