What Is The Density Of Each Of The Following Gases At STP?A. $C_3H_8$ B. $O_2$ C. Ne D. $NO_2$

Understanding the Density of Gases at Standard Temperature and Pressure (STP)

In chemistry, the density of a gas is an essential property that helps us understand its behavior and interactions. At Standard Temperature and Pressure (STP), the density of a gas is a critical parameter in various applications, including chemical reactions, gas mixtures, and industrial processes. In this article, we will explore the density of four gases at STP: propane ($C_3H_8$), oxygen ($O_2$), neon (Ne), and nitrogen dioxide ($NO_2$).

What is Standard Temperature and Pressure (STP)?

STP is a set of standard conditions used to express the properties of gases. It is defined as a temperature of 0°C (273.15 K) and a pressure of 1 atm (101.325 kPa). These conditions are used as a reference point to compare the properties of gases.

Calculating the Density of a Gas at STP

The density of a gas at STP can be calculated using the ideal gas law:

$$\rho = \frac{PM}{RT}$$

where:

• $\rho$ is the density of the gas (in kg/m³)
• $P$ is the pressure (in Pa)
• $M$ is the molar mass of the gas (in kg/mol)
• $R$ is the gas constant (in J/mol·K)
• $T$ is the temperature (in K)

Calculating the Density of Each Gas at STP

A. Propane ($C_3H_8$)

The molar mass of propane ($C_3H_8$) is 44.095 g/mol. Using the ideal gas law, we can calculate the density of propane at STP:

$$\rho = \frac{101325 \, \text{Pa} \times 44.095 \times 10^{-3} \, \text{kg/mol}}{8.314 \, \text{J/mol·K} \times 273.15 \, \text{K}}$$

$$\rho = 1.62 \, \text{kg/m}^3$$

B. Oxygen ($O_2$)

The molar mass of oxygen ($O_2$) is 32.00 g/mol. Using the ideal gas law, we can calculate the density of oxygen at STP:

$$\rho = \frac{101325 \, \text{Pa} \times 32.00 \times 10^{-3} \, \text{kg/mol}}{8.314 \, \text{J/mol·K} \times 273.15 \, \text{K}}$$

$$\rho = 1.33 \, \text{kg/m}^3$$

C. Neon (Ne)

The molar mass of neon (Ne) is 20.18 g/mol. Using the ideal gas law, we can calculate the density of neon at STP:

$$\rho = \frac{101325 \, \text{Pa} \times 20.18 \times 10^{-3} \, \text{kg/mol}}{8.314 \, \text{J/mol·K} \times 273.15 \, \text{K}}$$

$$\rho = 0.83 \, \text{kg/m}^3$$

D. Nitrogen Dioxide ($NO_2$)

The molar mass of nitrogen dioxide ($NO_2$) is 46.01 g/mol. Using the ideal gas law, we can calculate the density of nitrogen dioxide at STP:

$$\rho = \frac{101325 \, \text{Pa} \times 46.01 \times 10^{-3} \, \text{kg/mol}}{8.314 \, \text{J/mol·K} \times 273.15 \, \text{K}}$$

$$\rho = 1.73 \, \text{kg/m}^3$$

In conclusion, the density of each gas at STP can be calculated using the ideal gas law. The densities of propane ($C_3H_8$), oxygen ($O_2$), neon (Ne), and nitrogen dioxide ($NO_2$) at STP are 1.62 kg/m³, 1.33 kg/m³, 0.83 kg/m³, and 1.73 kg/m³, respectively. These values are essential in various applications, including chemical reactions, gas mixtures, and industrial processes.

• Ideal Gas Law: The ideal gas law is a fundamental equation in chemistry that relates the pressure, volume, and temperature of a gas.
• Molar Mass: The molar mass of a substance is the mass of one mole of that substance.
• Gas Constant: The gas constant is a fundamental constant in chemistry that relates the pressure, volume, and temperature of a gas.

• What is the density of a gas at STP?
  • The density of a gas at STP can be calculated using the ideal gas law.
• How do I calculate the density of a gas at STP?
  • You can use the ideal gas law to calculate the density of a gas at STP.
• What are the densities of propane, oxygen, neon, and nitrogen dioxide at STP?
  • The densities of propane, oxygen, neon, and nitrogen dioxide at STP are 1.62 kg/m³, 1.33 kg/m³, 0.83 kg/m³, and 1.73 kg/m³, respectively.
    Frequently Asked Questions (FAQs) About the Density of Gases at Standard Temperature and Pressure (STP)

A: The density of a gas at STP can be calculated using the ideal gas law. The ideal gas law is a fundamental equation in chemistry that relates the pressure, volume, and temperature of a gas.

A: To calculate the density of a gas at STP, you need to know the molar mass of the gas, the pressure, and the temperature. You can use the ideal gas law to calculate the density of the gas:

$$\rho = \frac{PM}{RT}$$

where:

• $\rho$ is the density of the gas (in kg/m³)
• $P$ is the pressure (in Pa)
• $M$ is the molar mass of the gas (in kg/mol)
• $R$ is the gas constant (in J/mol·K)
• $T$ is the temperature (in K)

A: The densities of propane, oxygen, neon, and nitrogen dioxide at STP are:

• Propane ($C_3H_8$): 1.62 kg/m³
• Oxygen ($O_2$): 1.33 kg/m³
• Neon (Ne): 0.83 kg/m³
• Nitrogen dioxide ($NO_2$): 1.73 kg/m³

A: To use the ideal gas law to calculate the density of a gas at STP, you need to know the molar mass of the gas, the pressure, and the temperature. You can plug these values into the ideal gas law equation:

$$\rho = \frac{PM}{RT}$$

A: The density of a gas at STP is an important property that can affect the behavior of the gas in various applications, including chemical reactions, gas mixtures, and industrial processes.

A: While the density of a gas at STP can provide some information about its behavior, it is not a reliable predictor of its behavior in other conditions. The behavior of a gas can be affected by many factors, including temperature, pressure, and the presence of other gases.

A: To convert the density of a gas from kg/m³ to other units, you can use the following conversion factors:

• 1 kg/m³ = 0.0624 lb/ft³
• 1 kg/m³ = 0.001940 slug/ft³
• 1 kg/m³ = 0.0001459 lb/in³

A: No, you cannot use the density of a gas at STP to calculate its molar mass. The molar mass of a gas is a fundamental property that can be determined experimentally or calculated from the atomic masses of its constituent atoms.

A: The molar mass of a gas can be determined experimentally by measuring its density and using the ideal gas law to calculate its molar mass. Alternatively, the molar mass of a gas can be calculated from the atomic masses of its constituent atoms.

A: While the density of a gas at STP can provide some information about its behavior, it is not a reliable predictor of its behavior in a mixture with other gases. The behavior of a gas in a mixture can be affected by many factors, including the presence of other gases, temperature, and pressure.

A: To calculate the density of a gas in a mixture with other gases, you need to know the molar masses of the gases, the pressure, and the temperature. You can use the ideal gas law to calculate the density of the gas in the mixture:

$$\rho = \frac{PM}{RT}$$

where:

• $\rho$ is the density of the gas in the mixture (in kg/m³)
• $P$ is the pressure (in Pa)
• $M$ is the molar mass of the gas (in kg/mol)
• $R$ is the gas constant (in J/mol·K)
• $T$ is the temperature (in K)

A: No, you cannot use the density of a gas at STP to predict its behavior in a mixture with other gases at different temperatures and pressures. The behavior of a gas in a mixture can be affected by many factors, including the presence of other gases, temperature, and pressure.

A: To calculate the density of a gas in a mixture with other gases at different temperatures and pressures, you need to know the molar masses of the gases, the pressure, and the temperature. You can use the ideal gas law to calculate the density of the gas in the mixture:

$$\rho = \frac{PM}{RT}$$

where:

• $\rho$ is the density of the gas in the mixture (in kg/m³)
• $P$ is the pressure (in Pa)
• $M$ is the molar mass of the gas (in kg/mol)
• $R$ is the gas constant (in J/mol·K)
• $T$ is the temperature (in K)

A: While the density of a gas at STP can provide some information about its behavior, it is not a reliable predictor of its behavior in a specific application. The behavior of a gas in a mixture can be affected by many factors, including the presence of other gases, temperature, and pressure.

A: To calculate the density of a gas in a mixture with other gases in a specific application, you need to know the molar masses of the gases, the pressure, and the temperature. You can use the ideal gas law to calculate the density of the gas in the mixture:

$$\rho = \frac{PM}{RT}$$

where:

• $\rho$ is the density of the gas in the mixture (in kg/m³)
• $P$ is the pressure (in Pa)
• $M$ is the molar mass of the gas (in kg/mol)
• $R$ is the gas constant (in J/mol·K)
• $T$ is the temperature (in K)

A: While the density of a gas at STP can provide some information about its behavior, it is not a reliable predictor of its behavior in a specific industry. The behavior of a gas in a mixture can be affected by many factors, including the presence of other gases, temperature, and pressure.

A: To calculate the density of a gas in a mixture with other gases in a specific industry, you need to know the molar masses of the gases, the pressure, and the temperature. You can use the ideal gas law to calculate the density of the gas in the mixture:

$$\rho = \frac{PM}{RT}$$

where:

• $\rho$ is the density of the gas in the mixture (in kg/m³)
• $P$ is the pressure (in Pa)
• $M$ is the molar mass of the gas (in kg/mol)
• $R$ is the gas constant (in J/mol·K)
• $T$ is the temperature (in K)

A: While the density of a gas at STP can provide some information about its behavior, it is not a reliable predictor of its behavior in a specific process. The behavior of a gas in a mixture can be affected by many factors, including the presence of other gases, temperature, and pressure.

A: To calculate the density of a gas in a mixture with other gases in a specific process, you need to know the molar masses of the gases, the pressure, and the temperature. You can use the ideal gas law to calculate the density of the gas in the mixture: