Choosing a basis of calculation means
Answer: A
One hundred moles of feed or one hour of operation turns a problem of ratios into one of definite numbers. The choice never affects the answer, only how much arithmetic is required. A convenient basis can shorten the work considerably.
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State whether the following is true or false.
The answer to a material balance depends on which basis was chosen.
Answer: B
The basis only scales the numbers, and any ratio or percentage in the answer is unchanged. Choosing a convenient basis is therefore a free decision that can be made purely for arithmetic. Percentages and ratios come out the same either way.
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For a stream whose composition is given in mole per cent, the most convenient basis is usually
Answer: C
Percentages then become the mole numbers directly and no conversion is needed at the outset. A mass basis is the right choice when the composition is given by mass. Matching the basis to the data saves a conversion step.
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A gas is 40 mole per cent methane of molar mass 16 and 60 mole per cent ethane of molar mass 30. What is its average molar mass?
Answer: D
Correct answer: 24.4
The average molar mass is the mole-fraction-weighted mean: \[ 0.4\times16 + 0.6\times30 = 6.4 + 18 = 24.4. \] Because the weights are *mole* fractions the answer must lie between 16 and 30 and nearer the ethane, which is what the 60 per cent implies - and the 23.0 offered is the unweighted average of the two, which would be right only for an equimolar mixture.
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Assertion (A): Average molar mass is computed with mole fractions rather than mass fractions.
Reason (R): The average is a total mass divided by a total number of moles, and mole fractions weight the moles correctly.
Answer: A
Both are true and the reason gives the arithmetic: using mass fractions computes the reciprocal average instead, which is a different and generally smaller number. A units check on the definition settles which weighting applies.
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Match each composition unit with what it is a ratio of.
List I
A. Mole fraction
B. Mass fraction
C. Molarity
D. Molality
List II
1. moles of solute to litres of solution
2. moles of a species to total moles
3. moles of solute to kilograms of solvent
4. mass of a species to total mass
Answer: B
Correct answer: A-2, B-4, C-1, D-3
Four composition units and four different denominators. Mole fraction is moles of a species over total moles, and mass fraction the same on a mass basis; both are dimensionless and both sum to one over the components. Molarity is moles of solute per litre of *solution*, and molality moles of solute per kilogram of *solvent* - a distinction that matters more than it first appears, as the next item shows.
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Molality is preferred to molarity in work over a range of temperatures because
Answer: C
Correct answer: the solvent mass does not change with temperature
Molarity has a volume in its denominator, and the solution expands as it warms, so a solution made up to 1 molar at 20 degrees is slightly less than 1 molar at 60. Molality is a ratio of two masses, both of which are temperature-independent, so the value is fixed once the solution is made. That is why colligative property work and any experiment over a temperature range uses molality.
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A solution contains 0.5 moles of solute in 2 kilograms of solvent. What is its molality?
Answer: D
Correct answer: 0.25 molal
\[ \frac{0.5\ \mathrm{mol}}{2\ \mathrm{kg}} = 0.25\ \mathrm{mol/kg}. \] The denominator is the mass of *solvent*, not of solution, which is what distinguishes molality from molarity in practice as well as in definition. Inverting the ratio gives the 4.0 offered.
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Consider the following statements about converting between mole and mass fractions.
1. The conversion requires the molar mass of every component.
2. Mole and mass fractions coincide when all molar masses are equal.
3. The conversion is a simple multiplication by a single factor.
Answer: A
The first two are correct. The third is wrong because each component is weighted by its own molar mass and the result renormalised, so no single factor can do the job for the whole stream. The molar masses enter individually rather than as an average.
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Arrange the steps of converting a mass per cent analysis to mole per cent.
1. total the moles obtained
2. take one hundred kilograms as the basis
3. divide each component by that total
4. divide each component mass by its molar mass
Answer: B
Choosing the basis first turns the percentages into masses, and the division by molar mass converts each to moles. Renormalising at the end is what makes the figures percentages again. The same four steps run in reverse for the other direction.
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