What volume of carbon dioxide measured at `27^(@)C` and `746.7` mm pressure will be obtained by treating `10.0 g` of pure marble with dilute hydrochloric acid ? (Aqueous tension at `27^(@)C` is `26.7 mm`)

Explanation

The chemical equation representing the reaction is :
`underset(100 g)(CaCO_(3))+2HCl rarr CaCl_(2)+H_(2)O+underset(22400 cm^(3)at STP)(CO_(2))`
Step 1. To calculate the volume of `CO_(2)` evolved from 10 g of `CaCO_(3)` at step.
From the chemical equation, 100 g of marble react to produce `22400 cm^(3)` of `CO_(2)` at STP
`therefore 10 g` of marble will produce `CO_(2)(22400)/(100)xx10=2240 cm^(3)`
This is the volume of `CO_(2)` evolved at STP.
Step 2. To calculate the volume of `CO_(2)` at `27^(@)C` and 746.7 mm pressure
`{:("Initial conditions","Final conditions"),(V_(1)=2240 cm^(3),V_(2)= ? cm^(3)),(P_(1)=760 mm, P_(2)=746.7-26.7=720 mm),(T_(1)=273 K,T_(2)=27+273=300 K):}`
Applying the gas equation, we have
`(V_(2)xx720)/(300)=(2240xx760)/(273)`
`V_(2)=(2240xx760)/(273)xx(300)/(720)=259.8 cm^(3)`
Thus, the volume of carbon dioxide obtained `= 2598.3 cm^(3)`.