Each hour 7% of Chemical A converts to Chemical B, and 6% of Chemical B converts to Chemical A. If initially there is 16 mg of Chemical A and 13 mg of Chemical B, what is the steady state weight of Chemical A (to 2 decimal places)?

Question

BlackTom AI · Accepted Answer

At steady state the net transfer between A and B is zero, so the flow from A to B equals the flow from B to A.

1) Relevant concepts:
- Conservation of total mass: conversions are only between A and B, so A + B stays constant at 16 + 13 = 29 mg.
- Steady-state (equilibrium) condition: fraction leaving A per hour (7%) equals fraction entering A from B per hour (6%), when expressed in terms of steady-state amounts.
- Simple algebra to solve two equations (or use ratios).

2) Step-by-step reasoning:
Let A* and B* be the steady-state amounts (mg). Each hour A loses 7% and gains 6% of B, so at equilibrium:
A* = 0.93 A* + 0.06 B*.
Rearrange: A* − 0.93 A* = 0.06 B* → 0.07 A* = 0.06 B*.

3) Intermediate calculations:
From 0.07 A* = 0.06 B* we get the ratio A*/B* = 0.06/0.07 = 6/7.
Write A* = 6k and B* = 7k for some k. Use conservation of mass: A* + B* = 13k = 29.
Solve for k: k = 29/13.
Thus A* = 6k = 6 × (29/13) = 174/13 = 13.384615... .

4) Why this is correct:
The algebra enforces zero net flow into A and uses the invariant total mass. The ratio 6:7 comes directly from the relative transfer rates (6% into A vs 7% out of A), so the steady split must be proportional to those numbers, scaled to the fixed total 29 mg.

5) Other options:
No multiple-choice options are given here. If alternatives ignored conservation or mis-solved the ratio (for example using 0.93/0.06 instead of 0.06/0.07), they would be incorrect.

6) Conclusion:
Rounded to two decimal places, A* = 13.384615... ≈ 13.38 mg. This matches the provided answer 13.38.

Each hour 7% of Chemical A converts to Chemical B, and 6% of Chemical B converts to Chemical A. If initially there is 16 mg of Chemical A and 13 mg of Chemical B, what is the steady state weight of Chemical A (to 2 decimal places)?Short answer

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