Question

How many litres of HCl gas, measured at 30.0 °C and 745 torr, are required to prepare 1.25 L of a 3.20M solution of hydrochloric acid?

Short answer

The volume of HCl gas measured at 30^oC and 745 torr= 102L.

Step-by-step solution

Definition

The ideal gas may be defined as a gas which follows the ideal gas equation under standard temperature and atmospheric pressure.

\(\begin{array}{*{20}{l}}{{\bf{PV = nRT}}}\\{{\bf{Where, P = Pressure of the gas}}}\\\begin{array}{l}{\bf{V = Volume of the gas, }}\\{\bf{n = Amount of substance, }}\\{\bf{R = ideal gas constant,}}\end{array}\\{{\bf{T = Temperature}}}\end{array}\)

Explanation for Ions Interaction

Ion interaction is when solute molecules interact with solvent molecules to form a solution.

According to the question, we will calculate the number of moles,

\(\begin{array}{l}{\rm{Molarity (mol }}{{\rm{L}}^{{\rm{ - 1}}}}{\rm{) = }}\frac{{{\rm{Number of moles (mol)}}}}{{{\rm{Volume of solution (L)}}}}\\{\rm{3}}{\rm{.20mol }}{{\rm{L}}^{{\rm{ - 1}}}}{\rm{ = }}\frac{{{\rm{x mol}}}}{{{\rm{1}}{\rm{.25L}}}}\\{\rm{x = 4}}{\rm{.00 mol HCl}}\end{array}\)

Using the ideal gas law,

Change pressure to atmospheric pressure and convert temperature from\({\rm{^\circ C}}\)to Kelvin

\(\begin{array}{l}{\rm{1atm/x = }}\frac{{{\rm{760tor}}}}{{{\rm{745tor}}}}\\{\rm{Value of pressure = 0}}{\rm{.9803 atm}}\\{\rm{V = }}\frac{{{\rm{nRT}}}}{{\rm{P}}}{\rm{\; = \;}}\frac{{{\rm{4mol \times 0}}{\rm{.08026atmL}}{{\rm{K}}^{{\rm{ - 1}}}}{\rm{mo}}{{\rm{l}}^{{\rm{ - 1}}}}{\rm{ \times 303}}{\rm{.15K}}}}{{{\rm{0}}{\rm{.9803atm}}}}\\{\rm{V = 102 L}}\end{array}\)