At S.T.P., the density of nitrogen monoxide is

Options

A. `3.0 gL^(-1)`
B. `30gL^(-1)`
C. `1.3 gL^(-1)`
D. `2.68 gL^(-1)`

Answer

To find the density of nitrogen monoxide (NO) at standard temperature and pressure (STP), we can use the ideal gas equation and the relationship between density, mass, and volume. Here’s a step-by-step solution:

### Step 1: Understand the Ideal Gas Equation
The ideal gas equation is given by:
\[ PV = nRT \]
where:
- \( P \) = pressure of the gas
- \( V \) = volume of the gas
- \( n \) = number of moles of the gas
- \( R \) = universal gas constant
- \( T \) = absolute temperature of the gas

### Step 2: Relate Moles to Mass
The number of moles \( n \) can be expressed in terms of mass \( m \) and molar mass \( M \):
\[ n = \frac{m}{M} \]
Substituting this into the ideal gas equation gives:
\[ PV = \frac{m}{M}RT \]

### Step 3: Rearrange the Equation
Rearranging the equation to express \( P \) in terms of \( m \) and \( V \):
\[ PM = \frac{m}{V}RT \]
Here, \( \frac{m}{V} \) is the density \( D \) of the gas. Thus, we can write:
\[ PM = DRT \]

### Step 4: Solve for Density
From the equation \( PM = DRT \), we can solve for density \( D \):
\[ D = \frac{PM}{RT} \]

### Step 5: Determine Molar Mass of Nitrogen Monoxide
The molar mass \( M \) of nitrogen monoxide (NO) is calculated as follows:
- Molar mass of Nitrogen (N) = 14 g/mol
- Molar mass of Oxygen (O) = 16 g/mol
Thus,
\[ M = 14 + 16 = 30 \text{ g/mol} \]

### Step 6: Substitute Values at STP
At STP:
- Pressure \( P = 1 \text{ atm} \)
- Temperature \( T = 273 \text{ K} \)
- Universal gas constant \( R = 0.0821 \text{ atm L/(K mol)} \)

Now substituting these values into the density equation:
\[ D = \frac{(1 \text{ atm})(30 \text{ g/mol})}{(0.0821 \text{ atm L/(K mol)})(273 \text{ K})} \]

### Step 7: Calculate Density
Now, performing the calculation:
\[ D = \frac{30}{0.0821 \times 273} \]
Calculating the denominator:
\[ 0.0821 \times 273 \approx 22.4143 \]
Thus,
\[ D = \frac{30}{22.4143} \approx 1.34 \text{ g/L} \]

### Conclusion
Therefore, the density of nitrogen monoxide at STP is approximately:
\[ D \approx 1.34 \text{ g/L} \]

### Final Answer
The density of nitrogen monoxide at STP is **1.34 g/L**.

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