Digital SATMath: AlgebraMedium
A scientist is studying a chemical reaction where the rate of reaction, R, is inversely proportional to the square of the concentration of one reactant, C. If the rate of reaction is 0.05 M/s when the concentration is 0.2 M, what is the rate of reaction when the concentration is 0.5 M?
- A0.008 M/s
- B0.016 M/s
- C0.04 M/s
- D0.025 M/s
Show answer & explanationAnswer & explanation
Correct answer: A. 0.008 M/s
Inversely proportional means R = k / C^2. Use the given values to find k: 0.05 = k / (0.2)^2. So, 0.05 = k / 0.04, which means k = 0.05 * 0.04 = 0.002. Now use k to find R when C = 0.5: R = 0.002 / (0.5)^2 = 0.002 / 0.25 = 0.008 M/s.
Why the other options are wrong
- B. This might result from an error in squaring the concentration or calculating k.
- C. This is likely an error in the constant of proportionality or the final division.
- D. This could arise from an incorrect inverse proportionality setup or calculation.
Inverse Proportionality (Squared)
A relationship where one quantity varies inversely with the square of another quantity, expressed as y = k/x^2.
- The constant of proportionality (k) is found by multiplying y by x^2.
- As x increases, y decreases rapidly.
- Used in physics and chemistry for relationships like inverse square law.
Memory trick: Inverse means Divide, constant 'k' connects the sides.