A stream is 30 per cent by mass of a solute with molar mass 60 in water of molar mass 18. Taking 100 kilograms as basis, what is the mole fraction of solute?
Answer: A
Thirty kilograms gives half a kilomole and seventy kilograms of water gives about three point nine, so the fraction is half over four point four. That is about eleven and a half per cent, well below the mass percentage.
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Assertion (A): Mole fraction is smaller than mass fraction for a heavy solute in a light solvent.
Reason (R): The heavy species contributes fewer moles per unit mass than the light one does.
Answer: B
Both are true and the reason gives the cause: dividing by a larger molar mass yields fewer moles, so the species counts for less on a mole basis than it does by weight. The effect is largest when the molar masses differ widely.
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A tie component in a material balance is one that
Answer: C
Nitrogen in a combustion calculation is the standard example, and it lets streams be related without solving the full set of equations. Identifying one early often shortens a problem dramatically. Looking for one is worth doing before writing any equations.
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State whether the following is true or false.
A component that reacts cannot serve as a tie component.
Answer: D
The whole value of a tie component is that its amount is the same on both sides, so a species that is consumed or produced breaks the relation. Inerts are therefore the usual candidates. Ash in a coal balance serves the same purpose.
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Consider the following statements about concentration in dilute aqueous solution.
1. Milligrams per litre and parts per million are nearly equal.
2. The approximation relies on the density being close to one kilogram per litre.
3. The same equality holds for a concentrated brine.
Answer: A
The first two are correct and the second explains the first. The third fails because a concentrated brine is appreciably denser than water, so the two measures diverge. The correction is simply the ratio of the densities.
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When a composition is quoted without stating its basis, the safest assumption is
Answer: B
Conventions differ between industries and a wrong assumption propagates silently through every subsequent step. Asking is cheaper than repeating the calculation, and the second option, though a common convention, is not universal.
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