Let's solve the problem step by step to find the density of the gas.
Given:
1. Molar mass (M) = 146.06 g/mol
2. Pressure (P) = 1.03 atm
3. Temperature (T) = 297 K
4. Universal gas constant (R) = 0.0821 L·atm/(K·mol)
We'll use the formula derived from the Ideal Gas Law to find the density (d) of the gas. The Ideal Gas Law is given by:
[tex]\[ PV = nRT \][/tex]
Where:
- [tex]\( P \)[/tex] is the pressure,
- [tex]\( V \)[/tex] is the volume,
- [tex]\( n \)[/tex] is the number of moles,
- [tex]\( R \)[/tex] is the universal gas constant,
- [tex]\( T \)[/tex] is the temperature.
To find the density, we use the equation:
[tex]\[ d = \frac{PM}{RT} \][/tex]
Where:
- [tex]\( d \)[/tex] is the density,
- [tex]\( P \)[/tex] is the pressure,
- [tex]\( M \)[/tex] is the molar mass,
- [tex]\( R \)[/tex] is the gas constant,
- [tex]\( T \)[/tex] is the temperature.
Steps:
1. Substitute the given values into the formula:
[tex]\[ d = \frac{1.03 \text{ atm} \times 146.06 \text{ g/mol}}{0.0821 \text{ L·atm/(K·mol)} \times 297 \text{ K}} \][/tex]
2. Calculate the value:
[tex]\[ d = \frac{1.03 \times 146.06}{0.0821 \times 297} \][/tex]
3. Perform the multiplications and division:
The result of the calculation will yield:
[tex]\[ d \approx 6.1698 \text{ g/L} \][/tex]
Therefore, the density of the gas is approximately 6.1698 g/L.
