Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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![**Question:**
A mixture of fluorine and chlorine effuse from a gas canister. Which gas effuses faster?
**Explanation:**
The rate of effusion of a gas is inversely proportional to the square root of its molar mass (Graham's Law of Effusion). The formula for comparing the rates of effusion of two gases is given by:
\[ \frac{Rate_1}{Rate_2} = \sqrt{\frac{M_2}{M_1}} \]
Where:
- \( Rate_1 \) and \( Rate_2 \) are the effusion rates of gases 1 and 2, respectively.
- \( M_1 \) and \( M_2 \) are the molar masses of gases 1 and 2, respectively.
To determine which gas will effuse faster, we can compare the molar masses of fluorine (F₂) and chlorine (Cl₂).
- Molar mass of \( F_2 \) = 2 * 18.998 g/mol = 37.996 g/mol
- Molar mass of \( Cl_2 \) = 2 * 35.453 g/mol = 70.906 g/mol
Applying Graham's Law of Effusion:
\[ \frac{Rate_{F_2}}{Rate_{Cl_2}} = \sqrt{\frac{M_{Cl_2}}{M_{F_2}}} \]
\[ \frac{Rate_{F_2}}{Rate_{Cl_2}} = \sqrt{\frac{70.906}{37.996}} \]
\[ \frac{Rate_{F_2}}{Rate_{Cl_2}} = \sqrt{1.866} \]
\[ \frac{Rate_{F_2}}{Rate_{Cl_2}} \approx 1.366 \]
This means that fluorine gas \( (F_2) \) effuses approximately 1.366 times faster than chlorine gas \( (Cl_2) \). Therefore, fluorine effuses faster than chlorine from the gas canister.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3d3fcad5-0847-4348-902e-95e13b235eb3%2Ff811242e-243d-434a-953a-87999bf4bd70%2Fnfgd2ud_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
A mixture of fluorine and chlorine effuse from a gas canister. Which gas effuses faster?
**Explanation:**
The rate of effusion of a gas is inversely proportional to the square root of its molar mass (Graham's Law of Effusion). The formula for comparing the rates of effusion of two gases is given by:
\[ \frac{Rate_1}{Rate_2} = \sqrt{\frac{M_2}{M_1}} \]
Where:
- \( Rate_1 \) and \( Rate_2 \) are the effusion rates of gases 1 and 2, respectively.
- \( M_1 \) and \( M_2 \) are the molar masses of gases 1 and 2, respectively.
To determine which gas will effuse faster, we can compare the molar masses of fluorine (F₂) and chlorine (Cl₂).
- Molar mass of \( F_2 \) = 2 * 18.998 g/mol = 37.996 g/mol
- Molar mass of \( Cl_2 \) = 2 * 35.453 g/mol = 70.906 g/mol
Applying Graham's Law of Effusion:
\[ \frac{Rate_{F_2}}{Rate_{Cl_2}} = \sqrt{\frac{M_{Cl_2}}{M_{F_2}}} \]
\[ \frac{Rate_{F_2}}{Rate_{Cl_2}} = \sqrt{\frac{70.906}{37.996}} \]
\[ \frac{Rate_{F_2}}{Rate_{Cl_2}} = \sqrt{1.866} \]
\[ \frac{Rate_{F_2}}{Rate_{Cl_2}} \approx 1.366 \]
This means that fluorine gas \( (F_2) \) effuses approximately 1.366 times faster than chlorine gas \( (Cl_2) \). Therefore, fluorine effuses faster than chlorine from the gas canister.
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