Question

1. the density of chlorine gas, cl₂, at 1.21 atm and 34.9°c is ______ g/l.

a. 0.0479 g/l
b. 0.295 g/l
c. 0.423 g/l
d. 1.70 g/l
e. 3.39 g/l

Explanation:

Step1: Convert temperature to Kelvin

$$T = 34.9+273.15=308.05\ K$$

Step2: Use the ideal gas law to find density formula

The ideal gas law is $PV = nRT$. Since $n=\frac{m}{M}$ (where $m$ is mass and $M$ is molar mass), we can rewrite it as $PV=\frac{m}{M}RT$. Then, density $
ho=\frac{m}{V}$, so $P=\frac{
ho RT}{M}$. Rearranging for $
ho$ gives $
ho=\frac{PM}{RT}$.
The molar mass of $Cl_2$ is $M = 70.90\ g/mol$, $R = 0.0821\ L\cdot atm/(mol\cdot K)$, $P = 1.21\ atm$, $T = 308.05\ K$.

Step3: Calculate density

$$ ho=\frac{1.21\times70.90}{0.0821\times308.05}$$

$$ ho=\frac{85.789}{25.282805}\approx3.39\ g/L$$

Answer:

E. 3.39 g/L