The mean kinetic energy of the molecules in a sample of H20 gas is 12x10^-19
J, calculate the mean velocity of a molecule and the temperature of the gas.
Please help need to know for exam tomorrow.
To calculate the mean velocity of a molecule in a gas, we can use the equation:
v = √(2 * E_k / m)
Where:
v is the mean velocity of the molecule,
E_k is the mean kinetic energy of the molecule,
m is the molar mass of the molecule.
In this case, we are dealing with H2O gas. The molar mass of H2O is 18 g/mol.
First, let's convert the given value of the mean kinetic energy into SI units:
E_k = 12 x 10^-19 J
Next, we need to convert the molar mass into kilograms:
m = 18 g/mol = 0.018 kg/mol
To find the mean velocity, we can substitute the values into the equation:
v = √(2 * E_k / m)
= √(2 * 12 x 10^-19 J / 0.018 kg/mol)
Calculating this expression gives us the mean velocity of a molecule in the H2O gas sample.
To calculate the temperature of the gas, we can use the equation:
E_k = (3/2) * k * T
Where:
E_k is the mean kinetic energy of the molecule,
k is Boltzmann's constant (1.38 x 10^-23 J/K),
T is the temperature of the gas in Kelvin.
We can rearrange the equation to solve for T:
T = (2 * E_k) / (3 * k)
Substituting the given value of the mean kinetic energy:
T = (2 * 12 x 10^-19 J) / (3 * 1.38 x 10^-23 J/K)
Calculating this expression gives us the temperature of the gas.
Note: Make sure to convert joules to kelvin by adding 273.15, as temperature is usually measured in Kelvin.
Hope this helps! Good luck on your exam tomorrow.