Question

Calculate the volume occupied by $5.0g$ of acetylene gas at ${50^ \circ }C$ and $740mm$ pressure? (Report the answer as nearest integer)

Answer 1

As the volume to be found out is that of a gas, and the temperature pressure and mass is given we can use the general gas equation. The chemical formula of acetylene gas is ${C_2}{H_2}$.
Formulas used: $PV = nRT$, where $P$ is the pressure, $V$ is the volume occupied by the gas, $n$ is the number of moles, $R$ is the Universal gas constant and $T$ is the temperature in kelvin.

Complete step by step answer:
In this problem as the volume of the gas is the one to be found out, we can use the general gas equation here.
By the general gas equation, $PV = nRT$, where $P$ is the pressure, $V$ is the volume occupied by the gas, $n$ is the number of moles, $R$ is the Universal gas constant and $T$ is the temperature in kelvin.
As the given molecular mass is provided we can then calculate the molecular mass of ${C_2}{H_2}$ and then substitute it in the equation, $PV = \dfrac{m}{M}RT$
The given mass $\left( m \right)$ is $5.0g$
The molecular mass $\left( M \right)$ is calculated by adding the atomic mass of the two carbon atoms and the two hydrogen atoms, $M = 2\left( {12} \right) + 2\left( 1 \right)$
$\Rightarrow M = 26$
The pressure should be converted to $atm$,
$P = 740mmHg$
$\Rightarrow P = \dfrac{{740}}{{760}} = {{0}}{{.974atm}}$
Next the temperature should be converted to kelvin,
$T = {50^ \circ }C + 273$
$\Rightarrow T = 323K$
$R$ is the Universal gas constant of the value $0.082$
Now substituting all the variables and constants in the general gas equation, we get,
$0.974 \times V = \dfrac{5}{{26}} \times 0.082 \times 323$
$\Rightarrow V = \dfrac{5}{{26}} \times 0.082 \times 323 \times \dfrac{1}{{0.974}}$
Simplifying the equation, we get,
$\Rightarrow V = \dfrac{{100646.8}}{{19240}}$
$\Rightarrow V = 5.231L$
As the question says to report the answer to the nearest integer, therefore the answer is that the volume occupied by $5.0g$ of acetylene gas at ${50^ \circ }C$ and $740mm$ pressure is $5.0L$.

Note: Acetylene is the simplest of all alkynes, and is a very important fuel, as when it combines with oxygen, it produces the hottest flame of all fuel gases, which makes it the ideal candidate for welding operations. It is also known as a chemical building block, as it forms the basis of preparation of many organic compounds.
Note that in this case, we have taken acetylene to behave like an ideal gas. All ideal gases will always occupy the same amount of volume ($22.4L$) at standard temperature ($298K$) and pressure ($1atm$). Note that when gases deviate from ideality, they are known as real gases, and their properties are found using different equations like the Van der Waals equation.