Question

The partial pressure of hydrogen in a flask containing 2 gram of Hydrogen and 32 grams of $S{{O}_{2}}$is ​:
A)$\dfrac{1}{16}\text{ of }{{\text{P}}_{t}}$
B)$\dfrac{1}{9}\text{ of }{{\text{P}}_{t}}$
C)$\dfrac{2}{3}\text{ of }{{\text{P}}_{t}}$

Answer 1

Partial pressure of any gas is the pressure it exists on the other gas is present in a mixture. The pressure is calculated within the container. To find the partial pressures, we should know the molar masses of hydrogen and sulphur-di-oxide. Also to determine the molar fraction of each atomic gas.

Complete answer:
To determine the partial pressure, we first need to find the mole fraction. The mole fraction of an atom is dependent on the molar mass of the atom.
We know that the molar masses of ${{H}_{2}}$gas is 2 g/mol and that of $S{{O}_{2}}$gas is 64 g/mol.
Calculation-
Firstly, let’s find the no. of moles and total no. of moles of the given atoms.
Given mass of ${{H}_{2}}$= 2 g/mol
Atomic mass of ${{H}_{2}}$= 2 gm
Given mass of $S{{O}_{2}}$= 32 g/mol
Atomic mass of $S{{O}_{2}}$= 64 gm
So, $\text{Number of moles }=\text{ }\dfrac{Given\text{ mass}}{Atomic\text{ mass}}$
$\text{Number of moles of }{{\text{H}}_{2}}\text{ }=\text{ }\dfrac{2}{2}\text{ = 1}$

& 2 \\\ & \\\ \end{aligned}}\text{ = 0}\text{.5}$$ Thus, $Total\text{ nu}mber\text{ of moles = }$$$\text{Number of moles of }{{\text{H}}_{2}}$$+ $$\text{Number of moles of S}{{\text{O}}_{2}}\text{ }$$ $$=\text{ }1\text{ }+\text{ }0.5\text{ }=\text{ }1.5\text{ }moles$$ Now we’ll calculate the Mole fraction of ${{H}_{2}}$, $$\begin{aligned} & Mole\text{ }fraction\text{ }of\text{ }{{\text{H}}_{2}}\text{ = }\dfrac{\text{Number of }moles\text{ of }{{\text{H}}_{2}}\text{ gas}}{Total\text{ number of moles of gas in mixture}} \\\ & =\text{ }\dfrac{1}{1.5} \\\ \end{aligned}$$ Multiplying both the numerator and denominator by 2, we get- $\begin{aligned} & =\text{ }\dfrac{1\times 2}{1.5\times 2} \\\ & =\text{ }\dfrac{2}{3} \\\ \end{aligned}$ Finally, let’s calculate the Partial pressure of Hydrogen gas $$\begin{aligned} & Partial\text{ }pressure\text{ }of\text{ }Hydrogen\text{ }gas\text{ = Mole fraction of }{{\text{H}}_{2}}\text{ gas }\times \text{ Total Pressure} \\\ & \text{= }\dfrac{2}{3}\text{ }\times \text{ Total pressure} \\\ \end{aligned}$$ Total pressure is abbreviated as ${{P}_{t}}$ Therefore, $$Partial\text{ }pressure\text{ }of\text{ }Hydrogen\text{ }gas\text{ = }\dfrac{2}{3}\text{ }\times \text{ }{{\text{P}}_{t}}$$ **The correct answer is OPTION C- $$Partial\text{ }pressure\text{ }of\text{ }Hydrogen\text{ }gas\text{ = }\dfrac{2}{3}\text{ of }{{\text{P}}_{t}}$$** **Note:** While calculating the atomic mass, always keep in mind that for a diatomic gas like ${{H}_{2}}$ the atomic mass is twice the atomic number of the element because atomic mass is the sum of the number of neutrons and protons. The neutron and proton each have 1 atomic mass unit (amu). Also, the mole fraction is the ratio of the number of moles of gas and the total number of moles of both gases.