Suppose that a chemist is mixing two acid solutions, one of...

Suppose that a chemist is mixing two acid solutions, one of $20 \%$ concentration and the other of $30 \%$ concentration. Which concentration could not be obtained?
A. $22 \%$
B. $24 \%$
C. $28 \%$
D. $32 \%$

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Key Concepts

Mixture Problems

Mixture problems involve combining two or more substances with different properties to obtain a mixture with a desired property. In the context of acid solutions, the overall concentration of the resulting mixture is determined by the amounts and concentrations of each component, which allows one to analyze what final concentrations can or cannot be achieved.

Weighted Average

The weighted average is a method used to calculate the final concentration when two different solutions are mixed. The final concentration is computed by taking the sum of the products of each component's concentration and its proportion in the mixture, then dividing by the total amount. This ensures that the resulting concentration falls between the individual concentrations of the solutions mixed.

Convex Combination

A convex combination refers to a specific type of weighted average where the weights (proportions) are non-negative and add up to one. This concept is crucial in mixture problems, as it guarantees that the resulting concentration will lie within the range defined by the individual solution concentrations, meaning that any target concentration must be achievable only if it is within this range.

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