A Container Holds 15.0 G Of Phosphorus Gas At A Pressure Of 2.0 Atm And A Temperature Of 20.0 Celsius. What Is The Density Of The Gas?A. 12.3 G/L B. 0.40 G/L C. 180 G/L D. 2.57 G/L
Introduction
In this article, we will explore the concept of density and how it applies to gases. We will use the example of phosphorus gas to calculate its density. The density of a substance is defined as its mass per unit volume. In the case of gases, the density is typically expressed in units of grams per liter (g/L). Understanding the density of a gas is crucial in various fields, including chemistry, physics, and engineering.
The Ideal Gas Law
To calculate the density of phosphorus gas, we need to use the ideal gas law, which is given by the equation:
PV = nRT
where:
- P is the pressure of the gas in atmospheres (atm)
- V is the volume of the gas in liters (L)
- n is the number of moles of the gas
- R is the gas constant, which is equal to 0.0821 L atm/mol K
- T is the temperature of the gas in Kelvin (K)
Converting Temperature to Kelvin
The temperature of the gas is given as 20.0 Celsius. To convert this temperature to Kelvin, we use the following equation:
T (K) = T (C) + 273.15
Substituting the given temperature, we get:
T (K) = 20.0 + 273.15 = 293.15 K
Calculating the Number of Moles
The mass of the phosphorus gas is given as 15.0 g. To calculate the number of moles, we need to know the molar mass of phosphorus. The molar mass of phosphorus is 30.97 g/mol. We can calculate the number of moles as follows:
n = mass / molar mass = 15.0 g / 30.97 g/mol = 0.484 mol
Calculating the Volume of the Gas
Now that we have the number of moles, we can use the ideal gas law to calculate the volume of the gas. Rearranging the ideal gas law to solve for V, we get:
V = nRT / P
Substituting the values, we get:
V = (0.484 mol) (0.0821 L atm/mol K) (293.15 K) / (2.0 atm) = 5.93 L
Calculating the Density of the Gas
Now that we have the volume of the gas, we can calculate the density as follows:
density = mass / volume = 15.0 g / 5.93 L = 2.53 g/L
Conclusion
In this article, we calculated the density of phosphorus gas using the ideal gas law. We first converted the temperature from Celsius to Kelvin, then calculated the number of moles using the molar mass of phosphorus. We then used the ideal gas law to calculate the volume of the gas, and finally calculated the density using the mass and volume. The calculated density is 2.53 g/L, which is closest to option D.
Answer
The correct answer is D. 2.57 g/L.
Discussion
This problem requires a good understanding of the ideal gas law and how to apply it to calculate the density of a gas. The student should be able to convert the temperature from Celsius to Kelvin, calculate the number of moles using the molar mass, and use the ideal gas law to calculate the volume of the gas. The student should also be able to calculate the density using the mass and volume.
Key Concepts
- Ideal gas law
- Density of a gas
- Molar mass of phosphorus
- Conversion of temperature from Celsius to Kelvin
- Calculation of number of moles
- Calculation of volume of gas
- Calculation of density of gas
Practice Problems
- A container holds 10.0 g of oxygen gas at a pressure of 1.0 atm and a temperature of 25.0 Celsius. What is the density of the gas?
- A container holds 20.0 g of nitrogen gas at a pressure of 2.0 atm and a temperature of 30.0 Celsius. What is the density of the gas?
- A container holds 15.0 g of carbon dioxide gas at a pressure of 1.5 atm and a temperature of 20.0 Celsius. What is the density of the gas?
Solutions
- The density of oxygen gas is 0.93 g/L.
- The density of nitrogen gas is 1.19 g/L.
- The density of carbon dioxide gas is 2.03 g/L.
Q&A: Understanding the Density of Gases =============================================
Introduction
In our previous article, we explored the concept of density and how it applies to gases. We used the example of phosphorus gas to calculate its density. In this article, we will answer some frequently asked questions related to the density of gases.
Q: What is the ideal gas law?
A: The ideal gas law is a fundamental equation that describes the behavior of gases. It is given by the equation:
PV = nRT
where:
- P is the pressure of the gas in atmospheres (atm)
- V is the volume of the gas in liters (L)
- n is the number of moles of the gas
- R is the gas constant, which is equal to 0.0821 L atm/mol K
- T is the temperature of the gas in Kelvin (K)
Q: How do I convert temperature from Celsius to Kelvin?
A: To convert temperature from Celsius to Kelvin, you can use the following equation:
T (K) = T (C) + 273.15
For example, if the temperature is 20.0 Celsius, the temperature in Kelvin is:
T (K) = 20.0 + 273.15 = 293.15 K
Q: How do I calculate the number of moles of a gas?
A: To calculate the number of moles of a gas, you need to know the mass of the gas and its molar mass. The molar mass is the mass of one mole of the gas. You can calculate the number of moles as follows:
n = mass / molar mass
For example, if the mass of phosphorus gas is 15.0 g and its molar mass is 30.97 g/mol, the number of moles is:
n = 15.0 g / 30.97 g/mol = 0.484 mol
Q: How do I calculate the volume of a gas?
A: To calculate the volume of a gas, you can use the ideal gas law. Rearranging the ideal gas law to solve for V, you get:
V = nRT / P
For example, if the number of moles of phosphorus gas is 0.484 mol, the temperature is 293.15 K, the pressure is 2.0 atm, and the gas constant is 0.0821 L atm/mol K, the volume is:
V = (0.484 mol) (0.0821 L atm/mol K) (293.15 K) / (2.0 atm) = 5.93 L
Q: How do I calculate the density of a gas?
A: To calculate the density of a gas, you need to know the mass and volume of the gas. You can calculate the density as follows:
density = mass / volume
For example, if the mass of phosphorus gas is 15.0 g and its volume is 5.93 L, the density is:
density = 15.0 g / 5.93 L = 2.53 g/L
Q: What are some common mistakes to avoid when calculating the density of a gas?
A: Some common mistakes to avoid when calculating the density of a gas include:
- Not converting the temperature from Celsius to Kelvin
- Not using the correct molar mass of the gas
- Not using the correct gas constant
- Not using the correct pressure and volume of the gas
- Not rounding the answer to the correct number of significant figures
Conclusion
In this article, we answered some frequently asked questions related to the density of gases. We covered topics such as the ideal gas law, converting temperature from Celsius to Kelvin, calculating the number of moles, calculating the volume of a gas, and calculating the density of a gas. We also discussed some common mistakes to avoid when calculating the density of a gas.
Key Concepts
- Ideal gas law
- Density of a gas
- Molar mass of a gas
- Conversion of temperature from Celsius to Kelvin
- Calculation of number of moles
- Calculation of volume of a gas
- Calculation of density of a gas
Practice Problems
- A container holds 10.0 g of oxygen gas at a pressure of 1.0 atm and a temperature of 25.0 Celsius. What is the density of the gas?
- A container holds 20.0 g of nitrogen gas at a pressure of 2.0 atm and a temperature of 30.0 Celsius. What is the density of the gas?
- A container holds 15.0 g of carbon dioxide gas at a pressure of 1.5 atm and a temperature of 20.0 Celsius. What is the density of the gas?
Solutions
- The density of oxygen gas is 0.93 g/L.
- The density of nitrogen gas is 1.19 g/L.
- The density of carbon dioxide gas is 2.03 g/L.