The masses of 1 mole of various gases are as follows: hydrogen about 2 grams, helium about 4 grams, nitrogen about 28 grams, oxygen about 32 grams and carbon dioxide about 44 grams. On the average how fast does a molecule of each gas move at 333 Celsius?
To determine the average speed of a gas molecule at a given temperature, we can use the root mean square (rms) speed formula:
v = sqrt((3 * k * T) / m)
where:
v = average speed of a gas molecule
k = Boltzmann's constant (1.38 * 10^-23 J/K)
T = temperature in Kelvin
m = molar mass of the gas
To solve the problem, we need to convert the given Celsius temperature to Kelvin. The conversion formula is:
T(K) = T(°C) + 273.15
So, for 333°C, the temperature in Kelvin is:
T = 333 + 273.15 = 606.15 K
Now, we can calculate the average speeds for each gas using their respective molar masses:
For hydrogen (m = 2 g/mol):
v_hydrogen = sqrt((3 * 1.38 * 10^-23 * 606.15) / 2)
For helium (m = 4 g/mol):
v_helium = sqrt((3 * 1.38 * 10^-23 * 606.15) / 4)
For nitrogen (m = 28 g/mol):
v_nitrogen = sqrt((3 * 1.38 * 10^-23 * 606.15) / 28)
For oxygen (m = 32 g/mol):
v_oxygen = sqrt((3 * 1.38 * 10^-23 * 606.15) / 32)
For carbon dioxide (m = 44 g/mol):
v_carbon_dioxide = sqrt((3 * 1.38 * 10^-23 * 606.15) / 44)
By plugging in the values and performing the calculations, you can find the average speeds of the gas molecules for each gas at 333°C.