Calculate pressure (at stp) in 10.0 l vessel after reaction of 1.0 l hydrochloric acid (concentration 35 % and density 1.28 g/cub. cm.) with 1.0 kg of limestone (calcium carbonate with 4.0 % inert impurities). yield of reaction 97 %.
2 hcl (aq)+ caco₃ (s)= cacl₂(aq)+ h₂o(l)+ co₂(g)

The pressure in the vessel is 13,3 atm.

Explanation:

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

The increase in the pressure of the vessel after the reaction is by formation of a gas (CO₂). So we have to find the produced moles of this gas and apply the gas ideal law to find the pressure.

We have to find the limit reactant, to do so, we have to calculate the moles of each reactant in the reaction, the one that have the less moles will be the limit reactant:

HCl:

1,0L × (35/100) × (1000 cm³/1L) × (1,28 g/ 1cm³) × (1mol HCl/ 36,46 g) ÷ 2mol

(Concentration)      (L to cm³)         (cm³ to g)      (g to mol)  (moles of reaction)

moles of HCl= 6,14 mol

CaCo₃:

   1,0 kg     ×       (96/100)                ×   (1000 g/1kg) × (1 mol/100,09g)

(Limestone) (CaCo₃ in limestone)          (kg to g)            (g to mol)

moles of CaCo₃= 9,59 mol

So, reactant limit is HCl

This reaction have a yield of 97%. So, the CO₂ moles are:

6,14 mol × 97÷ = 5,96 mol CO₂

The ideal gas formula to obtain pressure is:

P = nRT/V

Where: n = 5,96mol; R= 0,082 atm×L/mol×K; T = 273,15 (until STP conditions) and V= 10,0 L

Replacing this values in the equation the pressure is

P = 13,3 atm

I hope it helps!