Gases Worksheet 6a (Gen Chem)
What is the relationship between the root mean squared speed of carbon dioxide and hydrogen gas molecules at 25°C?
Is it possible for carbon dioxide to have the same root mean squared speed as hydrogen gas at a certain temperature?
Explanation:
The root mean squared speed of a gas is determined by its temperature and molecular mass. In this case, we are looking to find the temperature at which the root mean squared speed of carbon dioxide is equal to that of hydrogen gas at 25°C.
The formula for root mean squared speed is Vrms = sqrt(3kT/m), where Vrms is the root mean squared speed, k is the Boltzmann constant, T is the temperature in Kelvin, and m is the molecular mass.
Calculating the Temperature:
Given that the root mean squared speed of carbon dioxide is equal to that of hydrogen at 25°C (or 298 K), we can set up the equation: T_CO2/M_CO2 = T_H2/M_H2
By plugging in the respective molecular masses (44 g/mol for CO2 and 2 g/mol for H2) and the given temperature of 298 K for hydrogen, we can solve for the temperature of carbon dioxide.
After the calculations, we find that the temperature at which the root mean squared speed of carbon dioxide equals that of hydrogen at 25°C is approximately 6626 K or 6352°C.