An empty 2.10-L vessel weighs 92.00 g. After filling the vessel with 1.00 atm of a gas at 27.0 °C, the vessel weighs 96.65 g. What is the molar mass of the gas?A. 4.24 g/molB. 11.1 g/molC. 54.5 g/molD. 113 g/mol **Problem Statement:**An empty 2.10-L vessel weighs 92.00 g. After filling the vessel with 1.00 atm of a gas at 27.0 °C, the vessel weighs 96.65 g. What is the molar mass of the gas? **Options:**A. 4.24 g/mol B. 11.1 g/mol C. 54.5 g/mol D. 113 g/mol **Solution Explanation:**To solve this problem, we can use the ideal gas law and the definition of molar mass to find the answer.1. **Determine the Mass of the Gas:** - Mass of vessel with gas = 96.65 g - Mass of empty vessel = 92.00 g - Mass of gas = 96.65 g - 92.00 g = 4.65 g2. **Use the Ideal Gas Law:**\[ PV = nRT \]Where:- \( P \) is the pressure (1.00 atm),- \( V \) is the volume (2.10 L),- \( n \) is the number of moles,- \( R \) is the ideal gas constant (0.0821 L·atm/mol·K),- \( T \) is the temperature in Kelvin (27.0 °C = 300.15 K).3. **Calculate the Number of Moles (n):**Rearranging the ideal gas law to find moles:\[ n = \frac{PV}{RT} = \frac{(1.00 \, \text{atm}) \times (2.10 \, \text{L})}{(0.0821 \, \text{L·atm/mol·K}) \times (300.15 \, \text{K})} \]4. **Calculate the Molar Mass (M):**Molar mass \( M \) is calculated as mass of gas divided by the number of moles:\[ M = \frac{\text{mass of gas}}{n} \]Plug in the values:\[ M = \frac{4.65 \, \text{g}}{n} \]5. **Solve for Molar Mass Using Calculated \( n \).**Check which option matches the calculated molar mass value.

Answered: Image /qna-images/answer/6ae251bd-8cf0-4b5a-a4d3-9d6592f78cb9.jpg

An empty 2.10-L vessel weighs 92.00 g. After filling the vessel with 1.00 atm of a gas at 27.0 °C, the vessel weighs 96.65 g. What is the molar mass of the gas? A. 4.24 g/mol B. 11.1 g/mol C. 54.5 g/mol D. 113 g/mol

An empty 2.10-L vessel weighs 92.00 g. After filling the vessel with 1.00 atm of a gas at 27.0 °C, the vessel weighs 96.65 g. What is the molar mass of the gas? A. 4.24 g/mol B. 11.1 g/mol C. 54.5 g/mol D. 113 g/mol

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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