What are the mass fractions of water and methanol in an equimolar mixture of the

Question

What are the mass fractions of water and methanol in an equimolar mixture of these two substances? What are the mole fractions of water and methanol in a mixture whose mass fraction of methanol in water is equal to 0.4? 1 gram of sodium chloride and 1 gram of calcium chloride are simultaneously dissolved in one 1 kg of pure water. The two salts undergo complete dissociation in this aqueous solution. What the mole fractions of the sodium calcium and chloride ions in this aqueous solution? The mixing tank shown below initially contains 100 kg of pure water. Suddenly the two inlet valves and single outlet valve are opened. One of the input streams is of pure water. The other input stream is of pure methanol. The tank is well mixed, so that the mass fractions of the outlet stream is always the same as the mass fractions of the water in the tank. Compute the exit stream mass fractions that will finally be obtained in the tank. Develop an expression for the mass fractions of water and methanol in the tank at any time. How long does it take to reach a water mass fraction of 0.5 in the exit stream? At high temperatures phosphine (PH_3) dissociates into phosphorous and hydrogen by the following reaction: 4PH_3 rightarrow P_4 + 6 H_2 At 800 degree C the rate at which phosphine dissociate is 4.0x10^-6 C_PH_3, mol/L-s .The reaction occurs in a constant volume 10-L vessel and the initial concentration of phosphine is 5 mol/L. If 5 mol of the phosphine reacts, how much phosphorous and hydrogen is produced? Develop expressions for the number of moles of phosphine, phosphorous, and hydrogen present at any time, and determine how many hours it would take to produce 3 mol of P_4.

Explanation / Answer

Solved first three problems, please split the question to get the remaining answers

1) Molar mass of water = 16 + 1 * 2 = 18 gm/mol

Molar mass of CH3OH = 12 + 4 * 1 + 16 = 32 gm/mol

Mass fraction of water = 18/(18+32) = 18/50 = 0.36

Mass fraction of CH3OH = 1 - Mass fraction of water = 1 - 0.36 = 0.64

2) Molar mass of water = 18 gm/mol

Molar mass of methanol = 32 gm/mol

Let the mole fraction of water be x

then mole fraction of methanol will be (1-x)

Mass fraction = 0.4 = 18x/(18x+32-32x)

0.4 = 18x/(32-14x)

12.8 - 5.6x = 18x

23.6x = 12.8

x = 0.5423

Mole fraction of methanol = 1 - 0.5423 = 0.4577

3)

Number of moles of water = 1000/18 = 55.55 moles

Molar mass of NaCl = 23 + 35.5 = 58.5 gm/mol

Number of moles of NaCl = 1/58.5 = 0.01709 moles

Molar mass of CaCl2 = 40 + 2 * 35.5 = 111 gm/mol

Number of moles of CaCl2 = 1/111 = 9.009 * 10^(-3) moles

mole fraction of sodium = 0.01709/(0.01709+9.009*10^(-3) + 55.56) = 3.0745 * 10^(-4)

mole fraction of calcium = 9.009 * 10^(-3)/(0.01709+9.009*10^(-3) + 55.56) = 1.626 * 10^(-4)

mole fraction of Cl = mole fraction of sodium + 2 * mole fraction of Calcium

=> 6.3145 * 10^(-4)

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