What volume of carbon dioxide would be produced at 350degreeC and atm from the c

Question

What volume of carbon dioxide would be produced at 350degreeC and atm from the complete thermal decomposition of 1.00 kg of magnesium carbonate, MgCO_3? What is the density of carbon dioxide at this temperature? A compound which contains only carbon, hydrogen, and sulfur is burned in oxygen under such conditions that the individual volumes of the reactants and products can be measured at the same temperature and pressure. It is found that 3 volumes of the compound react with oxygen to yield 3 volumes of carbon dioxide, 3 volumes of sulfur dioxide, and 6 volumes of water vapor. What volume of oxygen is required for the combustion? What is the formula of the compound? Is this an empirical formula or a molecular formula?

Explanation / Answer

MgCO3 ---- > MgO + CO2

Given that; P = 1 atm, temperature = 350 C = 623 K amount of MgCO3 = 1.00 kg

Number of moles of MgCO3 = 1.00 *10^3 g/ 84.3 g/ mol

= 11.86 moles

The molar mass of MgCO3 = 84.3 g/mol             

1 mol MgCO3 produces 1 mol CO2
11.86 mol MgCO3 x (1 mol CO2 / 1 mol MgCO3) = 11.86 mol CO2

Now determine the volume of CO2 from gas law;

PV = n RT

V= n RT / P

V= 11.86* 0.08206 *623/ 1.00

= 606.45 L

= 606450 mL

Density = mass / Volume

Mass = number of moles * molar mass

= 11.86*44.0
=521.84 g

The molar mass of CO2 = 44.0 g/mol

density = mass / volume

= 521.84 g/ 606.45 L

= 0.860 g/ L

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