Material Balance Without Reaction Questions and Answers

Answer: A

Correct answer: input equals output for every species present

With no reaction nothing is created or destroyed, and at steady state nothing accumulates, so the general balance collapses to input equals output - and it does so for each species separately, not merely for the total. That per-species form is what supplies the several independent equations a flowsheet problem needs.

Answer: B

Correct answer: False

The total balance is the sum of the species balances, so it carries no information they do not already contain. Writing all the species balances and the total gives one equation more than there are independent relations, and only \( n \) of the \( n+1 \) may be counted. Forgetting that is a common way of appearing to have enough equations when the problem is in fact under-specified.

Answer: C

Each species gives one balance, and the total is their sum rather than an extra. Counting the total as an additional equation is the commonest reason a degrees of freedom analysis comes out wrong. Any one of the balances may be swapped for the total.

Answer: D

A result of zero means the problem is exactly specified, a positive value means more data are needed and a negative one signals an over-specification or an inconsistency. Doing this count first prevents a good deal of wasted algebra.

Answer: A

Correct answer: Both A and R are true, and R is the correct explanation of A

Both are true and the reason gives both benefits. Counting degrees of freedom before solving reveals whether the problem is determinate at all, which saves attempting the impossible, and unit by unit it identifies which unit has zero degrees of freedom and can therefore be solved first - giving a starting point and an order for the rest of the flowsheet.

Answer: B

Correct answer: A-2, B-4, C-1, D-3

Counting unknowns less independent equations: zero means the problem is exactly specified and has a unique solution; a positive count means more specifications are needed; a negative count means it is over-specified. The last case splits in two - if the extra data are consistent the surplus specifications are merely redundant, and if they are not, the data contain an error.

Answer: C

Twenty kilograms of solute plus twenty-five gives forty-five in a hundred and fifty kilograms, which is thirty per cent. Averaging the two percentages directly would give thirty-five and ignores the different flow rates.

Answer: D

The average must be weighted by the flow rates, and only equal flows make the simple average correct. This is the same weighting error that appears in averaging molar masses and in blending recipes. Equal flows are the only case where it happens to work.

Answer: A

A split changes only the flow rates, so a single balance fixes everything once the split fraction is known. A separator changes composition and needs a species balance for each component. Recognising the difference saves a great deal of algebra.

Answer: B

The first two are correct. The third is wrong for a splitter, because the species balances all reduce to the same relation once the compositions are known to be identical, so only one is independent. The split fraction is the single piece of information needed.