Question
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It takes gas A 2.3 times as long to effuse through an orifice as the s
amount of nitrogen. What is the molar mass of gas
It takes gas A 2.3 times as long to effuse through an orifice as the s
amount of nitrogen. What is the molar mass of gas
Ask by Gonzalez Vaughn. in Jordan
Dec 07,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
الكتلة المولية لغاز A هي حوالي 5.293 جرام/مول.
Solution
To find the molar mass of gas A, we can use the relationship between the effusion rates of two gases through an orifice. The effusion rate is inversely proportional to the square root of the molar mass of the gas.
Given:
- Gas A takes 2.3 times as long to effuse through an orifice as nitrogen (N2).
- The molar mass of nitrogen (N2) is approximately 28 g/mol.
Let’s denote the molar mass of gas A as
The relationship between the effusion rates can be expressed as:
Where:
-
is the time it takes for gas A to effuse through the orifice, -
is the time it takes for nitrogen to effuse through the orifice, -
is the molar mass of nitrogen (28 g/mol), -
is the molar mass of gas A (which we need to find).
Given that
Simplifying the equation:
To find the molar mass of gas A, we can rearrange the equation:
Now, let’s calculate the molar mass of gas A.
Calculate the value by following steps:
Calculate the value by following steps:
- step0: Calculate:
- step1: Convert the expressions:
- step2: Simplify the expression:
- step3: Rewrite the expression:
- step4: Evaluate the power:
The molar mass of gas A is approximately 5.293 g/mol.
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Simplify this solution Bonus Knowledge
To find the molar mass of gas A, we can employ Graham’s Law of Effusion. According to the law, the rate of effusion of a gas is inversely proportional to the square root of its molar mass. Given that gas A takes 2.3 times longer than nitrogen (which has a known molar mass of approximately 28 g/mol), we can express the relationship as follows:
Squaring both sides yields
Now, let’s think about how frequently gas effusion occurs in real life. For example, balloons filled with helium deflate faster than those filled with air because helium molecules are lighter and effuse more rapidly. This phenomenon explains why helium-filled balloons float but shrivel up quicker than their air-filled counterparts. Next time you see a floating balloon, remember that it’s all about the gas’s molar mass and effusion rates!
Also, sometimes the calculations can get a bit tricky, and common mistakes include neglecting to square both sides when dealing with rates of effusion, or mixing up the order of gases. To avoid that, it’s essential to keep track of which gas is being compared and to ensure that the relationship is correctly applied! Always double-check your work to catch any pesky mistakes!
