Question

The root-mean-square speed (thermal speed) of the molecules of a gas is 200m/s at 23.0°C. At 227°C the root-mean-square speed (thermal speed) of the molecules will be closest to (1) 160 m/s. (2) 330 m/s. (3) 260 m/s. (4) 630 m/s. (5) None of the above.

Answer 1

The root-mean-square speed of gas molecules is directly proportional to the square root of the temperature. To find the root-mean-square speed at a new temperature, we can use the equation V_rms2 = V_rms1 * √(T2/T1). Hence the correct answer is option 2

Step-by-step explanation:

The root-mean-square speed (thermal speed) of gas molecules is directly proportional to the square root of the temperature. In this case, the root-mean-square speed is 200 m/s at 23.0°C. To find the root-mean-square speed at 227°C, we can use the equation: V_rms2 = V_rms1 * √(T2/T1), where V_rms2 is the new root-mean-square speed, V_rms1 is the initial root-mean-square speed, T2 is the new temperature in Kelvin, and T1 is the initial temperature in Kelvin.

Let's solve the equation:

V_rms2 = 200 * √(500/296) = 200 * √(102/61) ≈ 330 m/s.

Therefore, the root-mean-square speed of the molecules at 227°C is closest to 330 m/s, so the correct answer is (2) 330 m/s.