What will be the density of carbon dioxide at `100^@C` and 800 mm Hg pressure ?

Explanation

To find the density of carbon dioxide (CO₂) at 100°C and 800 mm Hg pressure, we can follow these steps:

### Step 1: Convert the temperature from Celsius to Kelvin
To convert Celsius to Kelvin, we use the formula:
\[ T(K) = T(°C) + 273 \]
Given \( T = 100°C \):
\[ T = 100 + 273 = 373 \, K \]

### Step 2: Convert the pressure from mm Hg to atm
To convert mm Hg to atm, we use the conversion factor:
\[ 1 \, atm = 760 \, mm \, Hg \]
Thus, to convert 800 mm Hg to atm:
\[ P(atm) = \frac{800 \, mm \, Hg}{760 \, mm \, Hg/atm} \approx 1.0526 \, atm \]

### Step 3: Use the ideal gas equation to calculate density
The formula for density (\(d\)) in terms of pressure (\(P\)), molar mass (\(M\)), gas constant (\(R\)), and temperature (\(T\)) is:
\[ d = \frac{PM}{RT} \]
Where:
- \(P = 1.0526 \, atm\)
- \(M = 44.0 \, g/mol\) (molar mass of CO₂)
- \(R = 0.0821 \, atm \cdot L/(mol \cdot K)\) (universal gas constant)
- \(T = 373 \, K\)

### Step 4: Substitute the values into the density formula
Now we can substitute the values into the density formula:
\[ d = \frac{(1.0526 \, atm)(44.0 \, g/mol)}{(0.0821 \, atm \cdot L/(mol \cdot K))(373 \, K)} \]

### Step 5: Calculate the density
Calculating the numerator:
\[ 1.0526 \times 44.0 \approx 46.31 \, g \cdot atm/mol \]
Calculating the denominator:
\[ 0.0821 \times 373 \approx 30.6293 \, atm \cdot L/mol \]
Now, divide the numerator by the denominator:
\[ d \approx \frac{46.31 \, g \cdot atm/mol}{30.6293 \, atm \cdot L/mol} \approx 1.51 \, g/L \]

### Final Answer
The density of carbon dioxide (CO₂) at 100°C and 800 mm Hg pressure is approximately **1.51 g/L**.

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