Assuming it behaves as an ideal gas, calculate the density of nitrogen, N,, at STP. density: g/L

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Question 9

**Calculating the Density of Nitrogen Gas**

*Assuming it behaves as an ideal gas, calculate the density of nitrogen, N₂, at STP (Standard Temperature and Pressure).*

**Density Calculation:**

\[ \text{density:} \ \underline{\hspace{3cm}} \ \text{g/L} \]

---

To calculate the density of nitrogen gas (N₂) under standard temperature and pressure conditions (0°C and 1 atm), you can use the ideal gas law:

\[ PV = nRT \]

Where:
- \( P \) is the pressure (1 atm),
- \( V \) is the volume in liters,
- \( n \) is the number of moles,
- \( R \) is the ideal gas constant (0.0821 L·atm/mol·K),
- \( T \) is the temperature in Kelvin (273.15 K).

For one mole of an ideal gas at STP:

\[ V = \frac{RT}{P} = \frac{(0.0821 \ \text{L·atm/mol·K}) \times (273.15 \ \text{K})}{1 \ \text{atm}} \approx 22.414 \ \text{L/mol} \]

The molar mass of nitrogen gas (N₂) is approximately 28.02 g/mol.

**Density Calculation Steps:**

1. **Moles of Nitrogen (N₂):**  
   At STP, 1 mole of nitrogen gas occupies 22.414 L.

2. **Calculate Density:**  
   \[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} = \frac{28.02 \ \text{g/mol}}{22.414 \ \text{L/mol}} \approx 1.25 \ \text{g/L} \]

So, the density of nitrogen gas at STP is approximately 1.25 g/L.
Transcribed Image Text:**Calculating the Density of Nitrogen Gas** *Assuming it behaves as an ideal gas, calculate the density of nitrogen, N₂, at STP (Standard Temperature and Pressure).* **Density Calculation:** \[ \text{density:} \ \underline{\hspace{3cm}} \ \text{g/L} \] --- To calculate the density of nitrogen gas (N₂) under standard temperature and pressure conditions (0°C and 1 atm), you can use the ideal gas law: \[ PV = nRT \] Where: - \( P \) is the pressure (1 atm), - \( V \) is the volume in liters, - \( n \) is the number of moles, - \( R \) is the ideal gas constant (0.0821 L·atm/mol·K), - \( T \) is the temperature in Kelvin (273.15 K). For one mole of an ideal gas at STP: \[ V = \frac{RT}{P} = \frac{(0.0821 \ \text{L·atm/mol·K}) \times (273.15 \ \text{K})}{1 \ \text{atm}} \approx 22.414 \ \text{L/mol} \] The molar mass of nitrogen gas (N₂) is approximately 28.02 g/mol. **Density Calculation Steps:** 1. **Moles of Nitrogen (N₂):** At STP, 1 mole of nitrogen gas occupies 22.414 L. 2. **Calculate Density:** \[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} = \frac{28.02 \ \text{g/mol}}{22.414 \ \text{L/mol}} \approx 1.25 \ \text{g/L} \] So, the density of nitrogen gas at STP is approximately 1.25 g/L.
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