Question

14.) Carbon dioxide, which is recognized as the major contributor to global warming as a "greenhouse gas," is formed when fossil fuels are combusted, as in electrical power plants fueled by coal, oil, or natural gas. One potential way to reduce the amount of CO2 added to the atmosphere is to store it as a compressed gas in underground formations. Consider a 1000-megawatt coal-fired power plant that produces about 7×10⁶ tons of CO2 per year.

1 ton = 907.185 kg = 2000 lb

a)Assuming ideal gas behavior, 1.00 atm, and 37 ∘C, calculate the volume of CO2 produced by this power plant.

b)If the CO2 is stored underground as a liquid at 10 ∘C and 120 atm and a density of 1.2 g/cm3, what volume does it possess?

c)If it is stored underground as a gas at 34 ∘C and 90 atm , what volume does it occupy?

Answer 1

a) Given, mass(m) = 7 x 10⁶ tons = 7 x 10⁶ tons x ( 10⁶ g / 1 ton) = 7 x 10¹² g

and molar mass (M) for CO₂ = (12+2x16) g/mol= 44 g/mol

T = 37⁰C = (37+273) K = 310 K

P = 1.00 atm = 101325 Pa

Now, PV= nRT

=> PV = (m/M) RT , since n = (m/M)

=> V = (m/M) x RT/P

=> V = (7 x 10¹² g / 44g/mol) x (8.314 m³ Pa. K^-1 mol^-1 x 310 K / 101325 Pa)

=> V =(18041.38 x 10¹² / 4458300) m³

=> V = (18041380 x 10⁹ /4458300) m³ = 4.05 x 10⁹ m³

b) Given, density = 1.2 g/cm³ and mass (m) = 7 x 10¹² g (as in first case)

Now, density = mass /volume

=> volume = mass/density

=> volume =( 7 x 10¹² g / 1.2 g/cm³)

=> volume = 5.83 x 10¹² cm³

=> volume = 5.83 x 10¹² cm³ x (10^-6 m³ / 1 cm³) = 5.83 x 10⁶ m³

c) Given, P = 90 atm = 90 x 101325 Pa = 9119250 Pa = 9.1 x 10⁶ Pa

T = 34⁰C =(34+273) K = 307 K

Now,

PV= nRT

=> PV = (m/M) RT , since n = (m/M)

=> V = (m/M) x RT/P

=> V = (7 x 10¹² g / 44g/mol) x (8.314 m³ Pa. K^-1 mol^-1 x 307 K / 9.1 x 10⁶ Pa)

=> V = 17866.786 x 10¹² / 400.4 x 10⁶)m³

=> V = 44.6 x 10⁶ m³ = 4.46 x 10⁷ m³