The temperature must be raised to 2581.2°C to triple the RMS speed of the gas molecules.
To calculate the final temperature, we should square both sides of the equation:
Initial RMS Speed = √(3RT1/M)
Triple the RMS Speed = √(3RT2/M)
where:
R is the universal gas constant
T1 is the initial temperature in Kelvin
T2 is the final temperature in Kelvin
M is the molar mass of the gas
Squaring both sides:
(Triple the RMS Speed)^2 = (3RT2/M)^2
3^2 * (Initial RMS Speed)^2 = 3RT2/M
9 * (3RT1/M)^2 = 3RT2/M
Solving for T2:
T2 = 9 * T1 = 9 * 317.15 K = 2854.35 K
Converting Kelvin to Celsius:
T2 = 2854.35 K - 273.15 = 2581.2°C
Therefore, the temperature must be raised to 2581.2°C to triple the RMS speed of the gas molecules.