Question

question 5
calculate the density of co₂ gas at 20°c and 860 mm hg. (co₂ = 44.0 g/mol)
2.07 g/l
0.813 g/l
91.8 g/l
30.3 g/l
15730 g/l

Explanation:

Step1: Convert units

Convert pressure from mmHg to atm. Since \(1\ atm = 760\ mmHg\), then \(P=\frac{860}{760}\ atm\approx1.1316\ atm\). Convert temperature from \(^{\circ}C\) to \(K\), \(T=(20 + 273.15)K=293.15\ K\). The ideal - gas constant \(R = 0.0821\ L\cdot atm/(mol\cdot K)\), and molar mass \(M = 44.0\ g/mol\).

Step2: Use the density formula for ideal gas

The formula for the density of an ideal gas is \(
ho=\frac{PM}{RT}\). Substitute the values: \(
ho=\frac{1.1316\ atm\times44.0\ g/mol}{0.0821\ L\cdot atm/(mol\cdot K)\times293.15\ K}\).
First, calculate the numerator: \(1.1316\times44.0 = 49.7904\ g/(L\cdot K)\).
Then, calculate the denominator: \(0.0821\times293.15\approx24.0776\ L\cdot atm/(mol\cdot K)\).
Finally, \(
ho=\frac{49.7904}{24.0776}\ g/L\approx2.07\ g/L\).

Answer:

\(2.07\ g/L\)