RMS Speed Questions

Standard Temperature and Pressure (STP) is:

pressure of 1 atmosphere = 1.01 x 10⁵ Pa

temperature of 0°C = 273K

At STP 1 mole of ideal gas occupies 22.4 litres = 22.4 x 10^-3 m³

Q1. Calculate the RMS speed of air molecules in a container in which the pressure is 1.0 x 10⁵ Pa and the density of air is 1.3 kg m^-3.

Q2. The following table shows the distribution of the speeds of 20 particles:

Speed/ms^-1	10	20	30	40	50	60
Number of particles	1	3	8	5	2	1

Find

(a) the most probable speed,

(b) the average speed,

(c) the RMS speed.

Q3. The RMS speed of helium at STP is 1.30 km s^-1. Calculate the density of helium at STP.

Q4. The RMS speed of nitrogen molecules at 127^oC is 600 ms^-1. Calculate the RMS speed at 1127^oC.

Q5. If the density of nitrogen at STP is 1.25 kg m^-3, calculate the RMS speed of nitrogen at 227 °C.

Q6. Calculate the temperature in degrees Celsius at which the RMS speed of oxygen molecules is twice as great as their RMS speed at 27 °C.