Question

Answer the following for the reaction: CaCO3(s)+2HCl(aq)→H2O(l)+CO2(g)+CaCl2(aq)

What is the molarity of a HCl solution if the reaction of 215. mL of the HCl solution with excess CaCO3 produces 10.7 LL of CO2 gas at 725 mmHg and 18∘C?

Answer 1

Answer:

Step 1: Explanation

The ideal gas law is the equation of state of a hypothetical ideal gas. It is a good approximation of the behavior of many gases under many conditions.

We know the ideal gas equation,

PV=nRT

where, R=universal gas constant ( it may vary in unit like 0.08206 L-atm mol^-1 K^-1 , 62.36 torr-L mol^-1 K^-1 )

T=Temperature ( Unit = Kelvin )

P=Pressure ( Unit= atm )

V=Volume ( Unit=Litre )

n=moles ( Unit = mol )

Step 2: Calculation of moles of CO₂

Temperature(T) = 18 °C = (18 +273.15)K = 291.15 K

Pressure(P)  = 725 mmHg × (1 atm / 760 mmHg ) = 0.954 atm

[ Note: 1 atm = 760 mmHg]

Volume(V) = 10.7 L

moles(n) = we need to calculate

on substituting the value

=> PV = nRT

=> moles(n) = PV / RT = ( 0.954 atm ×10.7 L) / ( 0.08206 L-atm /mol-K  × 291.15 K ) = 0.42723 mol

Hence, moles of CO₂ = 0.42723 mol

Step 3: Calculate the moles of HCl

CaCO₃(s) + 2 HCl(aq)------> H₂O(l) + CO₂(g) + CaCl₂(aq)

From the equation we can see

1 moles of CO₂ produced from 2 moles of HCl

so, 0.42723 mol of CO₂ will produced from = ( 2 mol of HCl / 1 mol of CO₂ )  × 0.42723 mol = 0.85446 mol of HCl

Step 4: Calculation of molarity of HCl

Given,

moles of HCl = 0.85446 mol

Volume of HCl solution = 215 mL = 0.215 L

[ because 1 L=1000 mL so, 215 mL = ( 215 mL  × ( 1 L / 1000 mL) = 0.215 L ]

Since we know ,

molarity = moles of solute / volume of solution in L

=> molarity = 0.85446 mol /0.215 L = 3.974 M  

Hence, the molarity of HCl is 3.974 M