Five molecules have speeds of 2.8, 3.2, 5.8, 7.3, and 7.4 m/s.Their root-mean-square speed is closest to:
A)2.5 m/s
B)5.3 m/s
C)5.7 m/s
D)28 m/s
E)32 m/s

Question

Quizplus · Accepted Answer

The equation for root-mean-square speed is:

v(rms) = √[(v₁² + v₂² + v₃² + … + v(n)²)/n]

Where v₁, v₂, v₃, …, v(n) are the individual speeds of the molecules and n is the total number of molecules.

Plugging in the values:

v(rms) = √[(2.8² + 3.2² + 5.8² + 7.3² + 7.4²)/5]

v(rms) = √[(7.84 + 10.24 + 33.64 + 53.29 + 54.76)/5]

v(rms) = √[159.93/5]

v(rms) = √31.986

v(rms) ≈ 5.7 m/s

Therefore, the closest answer is C) 5.7 m/s.

Five Molecules Have Speeds of 2