Question

Calcium carbide reacts with water to produce acetylene $\left({\mathbf{C}}_{\mathbf{2}}{\mathbf{H}}_{\mathbf{2}}\right)$and calcium hydroxide. The acetylene is collected over water at $\mathbf{40}\mathbf{.}{\mathbf{0}}^{\mathbf{o}}\mathbf{C}$ under a total pressure of 0.9950 atm . The vapor pressure of water at this temperature is 0.0728 atm . Calculate the mass of acetylene per litre of “wet” acetylene collected in this way assuming ideal gas behavior.

Short answer

The mass per liter of acetylene is 0.9345 g.

Step-by-step solution

Given data

Total pressure of acetylene = 0.9950 atm

Vapor pressure of water = 0.0728 atm

$\mathrm{Volume}\left(\mathrm{V}\right)=1.0\mathrm{L}$

$R=0.08206 \text{Latm/Kmol}$

Concept of Ideal gas equation

The ideal gas law shows the relation between various parameters of the gas, pressure, volume, moles and temperature. The mathematical expression of ideal gas is: PV = nRT , Where

$$\begin{gathered} P=\mathrm{Pressure} \\ V=\mathrm{volume}\left(\mathrm{L}\right) \\ T=\mathrm{temperature} \\ R=\mathrm{gas}\mathrm{constant}\mathrm{L}.\mathrm{atm}/\mathrm{K}.\mathrm{mol} \end{gathered}$$

Calculation of  moles  of acetylene gas

Pressure due to acetylene gas$=(0.9950-0.0728)=0.9222\mathrm{atm}$

Using Ideal gas equation, we can write

$\begin{array}{rcl}n& =& \frac{PV}{R_T}\\ & =& \frac{(0.9222)\left(1\right)}{(0.08206)(313.15)}\\ & =& 0.0359\text{mol}\end{array}$

So, the number of moles of acetylene is 0.0359 mol

Calculation of  mass per liter of acetylene

Molar mass of acetylene = 26 g/mol

Mass per litre of acetylene $=0.0359\times 26=0.9335 \text{g}$

So, the mass per litre of acetylene = 0.9345 g