Question

Calcium carbide,$Ca{C_2}$, is an important preliminary chemical for industries producing synthetic fabrics and plastics. $Ca{C_2}$ may be produced by heating calcium oxide with coke. What is the amount of $Ca{C_2}$ which can be produced from the reaction of excess calcium oxide and $10.2g$ of carbon?
(assume $100\% $efficiency of reaction)
$CaO + C \to Ca{C_2} + CO$
A. $18.1g$
B.$28.4g$
C.$20.8g$
D.$27.4g$

Answer 1

Hint: We know that the atomic number of carbon is six. The mass of carbon is $12$. The molecular mass of calcium carbide is $64$. Firstly we will have to balance the chemical equation $CaO + C \to Ca{C_2} + CO$and analyse the equation to find out the number of moles of calcium oxide formed and the mass of calcium oxide produced.

Completes step by step solution:
We already know from the question that calcium oxide is in excess. We are given that only $10.2g$ of carbon is given. The reaction that we are given with is $CaO + C \to Ca{C_2} + CO$. It is not balanced, so the balanced equation will be $CaO + 3C \to Ca{C_2} + CO$. It is given that the chemical reaction is hundred percent efficient.
So three moles of carbon react to form one mole of calcium carbide. Mathematically we can write-
$
  3C \to 1Ca{C_2} \\
  1C \to \dfrac{1}{3}Ca{C_2} \\
 $
$10.2g$ of carbon is equal to $\dfrac{{10.2}}{{12}}moles$
$\dfrac{{10.2}}{{12}}moles$ of carbon will produce $\dfrac{{10.2}}{{12}} \times \dfrac{1}{3}$ moles of $Ca{C_2}$.
The molecular mass of calcium carbide will be $40 + 24 = 64g$
The mass of calcium carbide produced will be $ \Rightarrow \dfrac{{10.2}}{{12}} \times \dfrac{1}{3} \times 64 = 18.1g$
So from the above explanation and calculation it clear to us that the correct answer of the given question is option: $18.1g$

Hence, the correct answer option A.

Additional information:
Calcium oxide is a very important compound. It is used in the process of making cement. Calcium oxide is also known as quicklime. It is also used in the production of iron steel, paper and pulp, treatment of water and in mining industries.

Note: Always remember that when it is given that it is hundred percent efficient it means the yield percent is also hundred percent. Calcium carbide is a very important compound for fabric and plastics industries. Always solve the numerical carefully and avoid the silly mistakes.