Two gases effuse through a hole. Gas A has 9 times the molecular mass of gas B. What is the ratio of the two molecular speeds?
1/3
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To determine the ratio of the two molecular speeds, we can use Graham's law of effusion. Graham's law states that the rate of effusion for a gas is inversely proportional to the square root of its molar mass.
The rate of effusion can be represented by the molecular speed, as both are directly proportional. Therefore, the ratio of the two molecular speeds can be found by comparing the square root of their molecular masses.
Given that gas A has 9 times the molecular mass of gas B, we can denote the molecular masses as MA and MB, respectively. So, we have:
MA = 9MB
Taking the square root of both sides of the equation, we get:
√MA = √9MB
√MA = 3√MB
Therefore, the ratio of the two molecular speeds is 3:1.
In summary, the ratio of the two molecular speeds is 3:1, based on Graham's law of effusion, which relates the rate of effusion to the square root of the molar mass.