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what is the volume of 2.00x10^30 molecules of CO2, behaving as an ideal gas, with a pressure of 1800.0 mmHg, at room temperature (298 K)?

what is the volume of 2.00x10^30 molecules of CO2, behaving as an ideal gas, with a pressure of 1800.0 mmHg, at room temperature (298 K)?

Chemistry
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:** What is the volume of \(2.00 \times 10^{30}\) molecules of CO\(_2\), behaving as an ideal gas, with a pressure of 1800.0 mmHg, at room temperature (298 K)? --- This problem involves using 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 ideal gas constant (0.0821 L·atm/mol·K for this problem), - \( T \) is the temperature in Kelvin. ### Steps to Solve: 1. **Convert Pressure to atm:** \[ 1 \text{ atm} = 760 \text{ mmHg} \] \[ 1800.0 \text{ mmHg} = \frac{1800.0}{760} \text{ atm} \] 2. **Calculate Number of Moles (n):** Use Avogadro’s number (\(6.022 \times 10^{23}\) molecules/mol) to find moles: \[ n = \frac{2.00 \times 10^{30}}{6.022 \times 10^{23}} \text{ mol} \] 3. **Use Ideal Gas Law to Solve for Volume (V):** Substitute all known values into the ideal gas law and solve for \( V \). ### Graphs/Diagrams: There are no graphs or diagrams associated with this problem. The focus is on the calculation using the ideal gas law, guided by the given conditions of pressure, temperature, and quantity of molecules.
Transcribed Image Text:**Question:** What is the volume of \(2.00 \times 10^{30}\) molecules of CO\(_2\), behaving as an ideal gas, with a pressure of 1800.0 mmHg, at room temperature (298 K)? --- This problem involves using 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 ideal gas constant (0.0821 L·atm/mol·K for this problem), - \( T \) is the temperature in Kelvin. ### Steps to Solve: 1. **Convert Pressure to atm:** \[ 1 \text{ atm} = 760 \text{ mmHg} \] \[ 1800.0 \text{ mmHg} = \frac{1800.0}{760} \text{ atm} \] 2. **Calculate Number of Moles (n):** Use Avogadro’s number (\(6.022 \times 10^{23}\) molecules/mol) to find moles: \[ n = \frac{2.00 \times 10^{30}}{6.022 \times 10^{23}} \text{ mol} \] 3. **Use Ideal Gas Law to Solve for Volume (V):** Substitute all known values into the ideal gas law and solve for \( V \). ### Graphs/Diagrams: There are no graphs or diagrams associated with this problem. The focus is on the calculation using the ideal gas law, guided by the given conditions of pressure, temperature, and quantity of molecules.
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