PSAT Math Multiple-Choice Question 669: Answer and Explanation

Question: 669

The root mean squared speed of a molecule, v_rms, is calculated using the formula , where R is a gas constant, T is the temperature, and M is the molecular mass. The molecular mass of substance A is most likely to be less than the molecular mass of substance B if the temperature and v_rms of substance A compare in which ways to those of substance B ?

• A. Greater v_rms and lower temperature
• B. Lower v_rms and greater temperature
• C. Lower v_rms and equal temperature
• D. Cannot be determined

Correct Answer: A

Explanation:

(A) The relationship is easiest to see if you solve for M first. First, square both sides:

Multiply both sides by M to get M out of the denominator:

M(v_rms)² = 3RT

Now isolate M:

We can now consider how we can lower M. First, M is directly proportional to T. So decreasing T will decrease M. Further, M is inversely proportional to the square of v_rms. So increasing v_rms will decrease M because you will be dividing by a larger number. Therefore, choice (A) is correct.