Consider a mixture of several gases of identical masses Will

Consider a mixture of several gases of identical masses. Will all the mass fractions be identical? How about the mole fractions? The sum of the mole fractions for an ideal-gas mixture is equal to 1. Is this also true for a real-gas mixture? Somebody claims that the mass and mole fractions for a mixture of CO_2 and N_2O gases are identical. Is this true? Why? Consider a mixture of two gases. Can the apparent molar mass of this mixture be determined by simply taking the arithmetic average of the molar masses of the individual gases? When will this be the case? What is the apparent molar mass for a gas mixture? Does the mass of every molecule in the mixture equal the apparent molar mass? Is this statement correct? The temperature of an ideal-gas mixture is equal to the sum of the temperatures of each individual gas in the mixture. If not, how would you correct it? A rigid tank that contains 2 kg of N_2 at 25 degree C and 550 kPa is connected to another rigid tank that contains 4 kg of O_2 at 25 degree C and 150 kPa. The valve connecting the two tanks is opened, and the two gases are allowed to mix. If the final mixture temperature is 25 degree C, determine the volume of each tank and the final mixture pressure. Answers: 0.322 m3. 2.07 m3.204 kPa

Solution

a)

Yes, mass fractions will be identical because mass fraction = m_i / m and all the m_i are equal. Mole fractions need not be equal because m_i grams of each gas may have different number of moles depending on their Molar mass.

b)

Yes, even for real gas, some of all mole fractions will be 1.

c)

For CO2, molar mass = 12 + 2*16 = 44

For N2O, molar mass = 14*2 + 16 = 44

Since molar mass of both are equal, if the mass fraction is equal, mole fraction will also be equal. So the statement is true.

d)

Simply taking arithematic average to calculate apparent molar mass will not be right since molar masses may be different. Appropriate weightage need to be given for molar mass.

If the molar masses of all the gases in the mixture are equal, then we do simple arithematic average.