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solniwko [45]
3 years ago
7

Gaseous ethane will react with gaseous oxygen to produce gaseous carbon dioxide and gaseous water . Suppose 7.82 g of ethane is

mixed with 9.9 g of oxygen. Calculate the maximum mass of water that could be produced by the chemical reaction. Round your answer to significant digits
Chemistry
1 answer:
NeTakaya3 years ago
4 0

Answer:

4.79 g of water

Explanation:

From the reaction equation;

C2H6(g) + 7/2O2(g) ----> 2CO2(g) + 3H2O(g)

Next we convert the given masses of reactants to moles of reactants.

For ethane; number of moles = mass/molar mass= 7.82g/ 30gmol-1= 0.261 moles

For oxygen; number of moles= 9.9 g/32gmol-1= 0.31 moles

Next we determine the limiting reactant, the limiting reactant yields the least amount of product.

For ethane;

From the reaction equation,

1 mole of ethane yields 3 moles of water

0.261 moles of Ethan yields 0.261 ×3 = 0.783 moles of water

For oxygen;

3.5 moles of oxygen yields 3 moles of water

0.31 moles of oxygen yields 0.31 × 3/3.5 = 0.266 moles of water

Hence oxygen is the limiting reactant.

Mass of water produced = 0.266 moles of water × 18gmol-1 = 4.79 g of water

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<u>Answer:</u>

<u>For 1:</u> The standard Gibbs free energy change of the reaction is 10.60 kJ/mol

<u>For 2:</u> The equilibrium constant for the given reaction at 298 K is 1.386\times 10^{-2}

<u>For 3:</u> The equilibrium pressure of oxygen gas is 0.0577 atm

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The equation used to calculate standard Gibbs free energy change of a reaction is:

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\Delta G^o_f_{(M_2O_3(s))}=-10.60kJ/mol\\\Delta G^o_f_{(M(s))}=0kJ/mol\\\Delta G^o_f_{(O_2(g))}=0kJ/mol

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Hence, the standard Gibbs free energy change of the reaction is 10.60 kJ/mol

  • <u>For 2:</u>

Relation between standard Gibbs free energy and equilibrium constant follows:

\Delta G^o=-RT\ln K_{eq}

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\Delta G^o = Standard Gibbs free energy = 10.60 kJ/mol = 10600 J/mol    (Conversion factor: 1 kJ = 1000 J )

R = Gas constant = 8.314 J/K mol

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10600J/mol=-(8.314J/Kmol)\times 298K\times \ln (K_{eq})\\\\K_{eq}=1.386\times 10^{-2}

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The concentration of pure solids and pure liquids are taken as 1 in the expression. That is why, the concentration of metal and metal oxide is taken as 1 in the expression.

Putting values in above expression, we get:

1.386\times 10^{-2}=p_{O_2}^{3/2}\\\\p_{O_2}=0.0577atm

Hence, the equilibrium pressure of oxygen gas is 0.0577 atm

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