**Problem Statement:**A 0.597 g sample of an unknown compound occupies 245 mL at 305.6 K and 994.1 mmHg. What is the molar mass of the unknown compound?**Solution:**To find the molar mass of the unknown compound, we can use the Ideal Gas Law equation: \[ PV = nRT \]Where:- \( P \) is the pressure,- \( V \) is the volume,- \( n \) is the number of moles,- \( R \) is the universal gas constant, and- \( T \) is the temperature.**Given:**- Mass of the compound (\( m \)): 0.597 g- Volume (\( V \)): 245 mL = 0.245 L (since 1 L = 1000 mL)- Temperature (\( T \)): 305.6 K- Pressure (\( P \)): 994.1 mmHg- Universal gas constant (\( R \)): 0.0821 L·atm/(K·mol)First, convert the pressure from mmHg to atm:\[ P = 994.1 \, \text{mmHg} \times \frac{1 \, \text{atm}}{760 \, \text{mmHg}} = 1.307 \, \text{atm} \]Next, apply the Ideal Gas Law to solve for the number of moles (\( n \)):\[ n = \frac{PV}{RT} = \frac{(1.307 \, \text{atm}) \times (0.245 \, \text{L})}{(0.0821 \, \text{L·atm/(K·mol)}) \times (305.6 \, \text{K})} \]\[ n \approx 0.01289 \, \text{mol} \]Finally, calculate the molar mass (\( M \)) of the compound:\[ \text{Molar mass} = \frac{\text{mass}}{\text{moles}} = \frac{0.597 \, \text{g}}{0.01289 \, \text{mol}} \]\[ M \approx 46.34 \, \text{g/mol} \]**Conclusion:**The molar mass of the unknown

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A 0.597 g sample of an unknown compound occupies 245 mL at 305.6 K and 994.1 mmHg. What is the molar mass of the unknown compound?

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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Concept explainers

Mole Concept

Mole concept is a method to determine the amount of any substance that consists of some elemental particles using a grouping unit called ‘mole’. The mole concept enables one to handle the large amount of small elementary particles. The mole concept can be used in many calculations related to mole calculation, molar amount, mole ratio, and so on, which are significant in chemistry.

Question

**Problem Statement:**

A 0.597 g sample of an unknown compound occupies 245 mL at 305.6 K and 994.1 mmHg. What is the molar mass of the unknown compound?

**Solution:**

To find the molar mass of the unknown compound, we can use the Ideal Gas Law equation:

\[ PV = nRT \]

Where:
- \( P \) is the pressure,
- \( V \) is the volume,
- \( n \) is the number of moles,
- \( R \) is the universal gas constant, and
- \( T \) is the temperature.

**Given:**
- Mass of the compound (\( m \)): 0.597 g
- Volume (\( V \)): 245 mL = 0.245 L (since 1 L = 1000 mL)
- Temperature (\( T \)): 305.6 K
- Pressure (\( P \)): 994.1 mmHg
- Universal gas constant (\( R \)): 0.0821 L·atm/(K·mol)

First, convert the pressure from mmHg to atm:
\[ P = 994.1 \, \text{mmHg} \times \frac{1 \, \text{atm}}{760 \, \text{mmHg}} = 1.307 \, \text{atm} \]

Next, apply the Ideal Gas Law to solve for the number of moles (\( n \)):
\[ n = \frac{PV}{RT} = \frac{(1.307 \, \text{atm}) \times (0.245 \, \text{L})}{(0.0821 \, \text{L·atm/(K·mol)}) \times (305.6 \, \text{K})} \]

\[ n \approx 0.01289 \, \text{mol} \]

Finally, calculate the molar mass (\( M \)) of the compound:
\[ \text{Molar mass} = \frac{\text{mass}}{\text{moles}} = \frac{0.597 \, \text{g}}{0.01289 \, \text{mol}} \]

\[ M \approx 46.34 \, \text{g/mol} \]

**Conclusion:**
The molar mass of the unknown

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