Question

The calcium carbonate in limestone reacts with HCl to produce a calcium chloride solution and carbon dioxide gas:

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

EXPRESS YOUR ANSWER WITH THE APPROPRIATE UNITS.

a) How many milliliters of 0.200 MHCl can react with 7.25 g CaCO3?

b) How many moles of CO2 form when 27.5 mL of 3.00 M HCl react?

c) What is the molarity of a HClsolution if the reaction of 205 mLof the HCl solution with excess CaCO3 produces 14.0 L of CO2gas at 725 mmHg and 18∘C?

Answer 1

First calculate mole of CaCO₃

molar mass of CaCO₃ = 100 .0869 gm/mol then 7.25 gm = 7.25 / 100.0869 = 0.072437 mole

According to reaction 1 mole of CaCO₃ require to mole of HCl then 0.072437 mole of CaCO₃ require

0.072437 2 = 0.144874 mole of HCl

volume of solution in liter = no. of mole / molarity

volume of solution of HCl = 0.144874/0.200 = 0.72437 L = 724.37 ml

724.37 ml 0.200 M solution of HCl required

b) calculate mole of HCl

no. of mole = molarity volume of solution in liter

mole of HCl = 3 M 0.0275 L = 0.0825 mole of HCl

According to reaction 2 mole of HCl produce 1 mole of CO₂ then 0.0825 mole of HCl produce 0.0825/2 = 0.04125 mole of CO₂

c) Calculate mole of CO₂ produced by using ideal gas equation

Ideal gas equation

PV = nRT             where, P = atm pressure= 725.mmHg = 0.953948 atm,

V = volume in Liter = 14 L

n = number of mole = ?

R = 0.08205L atm mol^-1 K^-1 =Proportionality constant = gas constant,

T = Temperature in K = 18⁰C = 273.15+ 18 = 291.15 K

We can write ideal gas equation

n = PV/RT

Substitute the value

n = (0.953948   14)/(0.08205 291.15) = 0.559 mole

0.559 mole of CO₂ produced

According to reaction 2 mole of HCl required to produce 1 mole of CO₂ then to produce 0.559 mole require 0.559 2 = 1.118 mole of HCl

molarity = no. of mole / volume of solution in liter

molarity of HCl = 1.118/0.205 L = 5.454 M

molarity of HCl = 5.454 M