Find the temperature at which the root-mean-square speed of oxygen molecules would have the value of 640 ms-1 [1 kilomole of oxygen has a mass of 32 kg].
To find the temperature at which the root-mean-square (rms) speed of oxygen molecules would have a value of 640 m/s, we can use the equation for calculating the rms speed:
rms speed = √(3 * k * T / m)
where:
- rms speed is the root-mean-square speed of the gas molecules
- k is the Boltzmann constant (1.38 x 10^-23 J/K)
- T is the temperature in Kelvin
- m is the molar mass of the gas molecules
We can rearrange the equation to solve for T:
T = (rms speed)^2 * m / (3 * k)
Given that 1 kilomole of oxygen has a mass of 32 kg, we can convert this to grams:
mass = 32 kg = 32 * 1000 g = 32000 g
Plugging in the values into the equation:
T = (640 m/s)^2 * 32000 g / (3 * 1.38 x 10^-23 J/K)
= (640^2 * 32000) / (3 * 1.38 x 10^-23) K
= 83635200 / (3 * 1.38 x 10^-23) K
Calculating this expression:
T ≈ 5.67 x 10^24 K
Therefore, the temperature at which the root-mean-square speed of oxygen molecules would have the value of 640 m/s is approximately 5.67 x 10^24 K.