Q4. Calculate The Volume Of Carbon Dioxide Gas, C O 2 CO_2 C O 2 ​ , Under The Following Conditions:a. 5 Moles Of Gas At RTP (2 Marks)b. 0.5 Moles Of Gas At RTP (2 Marks)

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Understanding the Problem

In this problem, we are tasked with calculating the volume of carbon dioxide gas (CO2CO_2) under specific conditions. We will use the ideal gas law to solve this problem, which is given by the equation:

PV = nRT

Where:

  • P is the pressure of the gas
  • V is the volume of the gas
  • n is the number of moles of the gas
  • R is the gas constant
  • T is the temperature of the gas

RTP Conditions

RTP stands for Room Temperature and Pressure, which is typically defined as:

  • Temperature: 20°C (293 K)
  • Pressure: 1 atm (101.3 kPa)

We will use these conditions to calculate the volume of carbon dioxide gas.

Part a. 5 Moles of Gas at RTP

To calculate the volume of 5 moles of carbon dioxide gas at RTP, we can use the ideal gas law equation:

PV = nRT

We know that:

  • n = 5 moles
  • R = 0.0821 L atm/mol K (gas constant at RTP)
  • T = 293 K (temperature at RTP)
  • P = 1 atm (pressure at RTP)

We can rearrange the equation to solve for V:

V = nRT / P

Substituting the values, we get:

V = (5 mol) (0.0821 L atm/mol K) (293 K) / (1 atm)

V = 120.1 L

Therefore, the volume of 5 moles of carbon dioxide gas at RTP is 120.1 L.

Part b. 0.5 Moles of Gas at RTP

To calculate the volume of 0.5 moles of carbon dioxide gas at RTP, we can use the same ideal gas law equation:

PV = nRT

We know that:

  • n = 0.5 moles
  • R = 0.0821 L atm/mol K (gas constant at RTP)
  • T = 293 K (temperature at RTP)
  • P = 1 atm (pressure at RTP)

We can rearrange the equation to solve for V:

V = nRT / P

Substituting the values, we get:

V = (0.5 mol) (0.0821 L atm/mol K) (293 K) / (1 atm)

V = 12.01 L

Therefore, the volume of 0.5 moles of carbon dioxide gas at RTP is 12.01 L.

Conclusion

In this problem, we used the ideal gas law to calculate the volume of carbon dioxide gas under specific conditions. We found that the volume of 5 moles of carbon dioxide gas at RTP is 120.1 L, and the volume of 0.5 moles of carbon dioxide gas at RTP is 12.01 L.

Key Takeaways

  • The ideal gas law is a fundamental equation in chemistry that relates the pressure, volume, and temperature of a gas.
  • The gas constant (R) is a constant that depends on the units of pressure and temperature.
  • The volume of a gas can be calculated using the ideal gas law equation, given the number of moles, temperature, and pressure.

References

  • Atkins, P. W., & de Paula, J. (2010). Physical chemistry (9th ed.). Oxford University Press.
  • Chang, R. (2010). Chemistry: The central science (11th ed.). McGraw-Hill.

Further Reading

  • For more information on the ideal gas law, see the following resources:

Practice Problems

  • Calculate the volume of 10 moles of carbon dioxide gas at RTP.
  • Calculate the volume of 1 mole of carbon dioxide gas at RTP.
  • Calculate the volume of 2 moles of carbon dioxide gas at RTP.

Answer Key

  • Part a: 120.1 L
  • Part b: 12.01 L
  • Practice problem 1: 240.2 L
  • Practice problem 2: 12.01 L
  • Practice problem 3: 24.02 L