Question

What is the mass of $7.0L$ of hydrogen gas?

Answer 1

Hint: We can calculate the mass of any gas from the pressure, volume and temperature. When we have the values of pressure, volume, and temperature, we can calculate the moles of the gas. From the moles of the gas, we can calculate the mass of the gas using molar mass.

Complete step by step answer:
We know that for an ideal gas at standard temperature and pressure, the pressure of the gas is one atmosphere and temperature is $273.15K$.
We know that the expression of ideal gas is given as,
$PV = nRT$
Here, the pressure is represented as P.
Temperature is represented as T.
Volume is represented as V.
R is universal gas.
The number of moles of the gas is represented as n.
We can calculate the number of moles of the gas by rearranging the equation,
$PV = nRT$
$n = \dfrac{{PV}}{{RT}}$
Let us now substitute the values of temperature, pressure, volume and universal gas in the equation of ideal gas to get the number of moles.
The number of moles is calculated as,
$n = \dfrac{{PV}}{{RT}}$
We can substitute the known values we get,
$n = \dfrac{{\left( {1.00atm} \right)\left( {7.0L} \right)}}{{\left( {0.0821\,\dfrac{{atm \cdot L}}{{mol \cdot K}}} \right)\left( {273.15K} \right)}}$
On simplification we get_,
$n = 0.31\,mol$
We have calculated the moles of hydrogen gas as $0.31mol$.
Now, we can calculate the mass of hydrogen gas by multiplying the moles of hydrogen gas with the molar mass of hydrogen gas.
We know that the molar mass of hydrogen gas is $2.0g/mol$.
The mass of hydrogen gas is calculated as,
$Mass = Moles \times Molar\,mass$
We can substitute the known values we get,
$Mass = 0.31\,moles \times 2.0\,\dfrac{g}{{mol}}$
On simplification we get
$Mass = 0.62\,g$
We have calculated the mass of $7.0L$ of hydrogen gas is $0.62\,g$.

Note: We can also calculate the mass of $7.0L$ of hydrogen gas using the molar volume. We have to know that at standard temperature and pressure, one mole of any gas accommodates$22.4L$. So, we can calculate the moles of $7.0L$of hydrogen gas is calculated as,
$Moles = \dfrac{{Given\,volume}}{{Molar\,Volume}}$
$Moles = \dfrac{{7.0L}}{{22.4\,mol/L}} = 0.31\,mol$
We have calculated the moles of hydrogen gas as $0.31mol$.
Now, we can calculate the mass of hydrogen gas by multiplying the moles of hydrogen gas with the molar mass of hydrogen gas.
We know that the molar mass of hydrogen gas is $2.0g/mol$.
The mass of hydrogen gas is calculated as,
$Mass = Moles \times Molar\,mass$
$Mass = 0.31\,moles \times 2.0\,\dfrac{g}{{mol}}$
$Mass = 0.62\,g$
We have calculated the mass of $7.0L$ of hydrogen gas is $0.62\,g$.