Question

calculate the density of co₂ gas at 20°c and 860 mm hg. (co₂ = 44.0 g/mol)
○ 91.8 g/l
○ 2.07 g/l
○ 15730 g/l
○ 0.813 g/l
○ 30.3 g/l

Explanation:

Step1: Convert units

• Convert pressure from \(mmHg\) to \(atm\): \(P = \frac{860}{760}atm\approx1.13atm\)
• Convert temperature from \(^{\circ}C\) to \(K\): \(T=(20 + 273)K = 293K\)
• Molar mass of \(CO_2\), \(M = 44.0g/mol\)
• Ideal gas constant \(R=0.0821L\cdot atm/(mol\cdot K)\)

Step2: Use the density formula for ideal gas

The formula for density of an ideal gas is \(
ho=\frac{PM}{RT}\)
Substitute the values:
\(
ho=\frac{1.13atm\times44.0g/mol}{0.0821L\cdot atm/(mol\cdot K)\times293K}\)
First calculate the numerator: \(1.13\times44.0 = 49.72\)
Then calculate the denominator: \(0.0821\times293=24.0553\)
\(
ho=\frac{49.72}{24.0553}g/L\approx2.07g/L\)

Answer:

\(2.07g/L\)