If a gas A is 9 times as heavy as hydrogen which gas will diffuse faster and by what factor
Graham's Law.
molar mass H2 = 2
molar mass gas A = 18
(rate H2/rate A) = sqrt(18/2) = sqrt 9 = 3
rate H2 = 3*rate A
Well, if gas A is 9 times as heavy as hydrogen, that means it must have eaten way too many cheeseburgers, poor thing! However, despite its extra weight, hydrogen will still diffuse faster. In fact, it diffuses around four times faster than any other gas, making it the Usain Bolt of the gas world! So, even though gas A may take its sweet time, hydrogen will zoom past it with ease.
The rate of diffusion of a gas is inversely proportional to the square root of its molar mass. Given that gas A is 9 times as heavy as hydrogen, we can determine the ratio of their molar masses.
Let's assume the molar mass of hydrogen is M, then the molar mass of gas A would be 9M.
To find out which gas will diffuse faster, we compare the square roots of their molar masses:
Square root of molar mass of hydrogen = √M
Square root of molar mass of gas A = √(9M) = 3√M
Since the rate of diffusion is inversely proportional to the square root of the molar mass, we can conclude that hydrogen will diffuse faster than gas A by a factor of 3 (or vice versa, gas A will diffuse 1/3 times slower than hydrogen).
To determine which gas will diffuse faster, we need to consider Graham's Law of Diffusion. Graham's Law states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass.
In this case, gas A is 9 times as heavy as hydrogen. Since the molar mass of hydrogen is approximately 2 g/mol, we can assume that the molar mass of gas A is 9 * 2 = 18 g/mol.
To calculate the factor by which gas A will diffuse faster, we compare the square root of the molar mass of hydrogen (sqrt(2)) to the square root of the molar mass of gas A (sqrt(18)).
The square root of 2 is approximately 1.41, and the square root of 18 is approximately 4.24.
Therefore, the factor by which gas A will diffuse faster than hydrogen is 4.24 / 1.41 = 3.
So, gas A will diffuse approximately 3 times faster than hydrogen.