Question

Use the problem below to answer the question: When a current is passed through a solution of salt water, sodium chloride decomposes according to the following reaction: 2NaCl + 2H2O → 2NaOH + Cl2 + H2. How many grams of chlorine gas, Cl2, are given off if 7.5 grams of sodium chloride, NaCl, are decomposed? The molecular mass of NaCl is 58.44 g/mole. The molecular mass of Cl2 is 70.90 g/mole.

Answer 1

Answer : The mass of chlorine gas given off are 4.54 grams.

Solution : Given,

Mass of $NaCl$ = 7.5 g

Molar mass of $NaCl$ = 58.44 g/mole

Molar mass of $Cl_2$ = 70.90 g/mole

First we have to calculate the moles of $NaCl$.

$\text{ Moles of }NaCl=\frac{\text{ Mass of }NaCl}{\text{ Molar mass of }NaCl}=\frac{7.5g}{58.44g/mole}=0.128moles$

Now we have to calculate the moles of $Cl_2$

The balanced chemical reaction is,

$2NaCl+2H_2O\rightarrow 2NaOH+Cl_2+H_2$

From the balanced reaction we conclude that

As, 2 mole of $NaCl$ react to give 1 mole of $Cl_2$

So, 0.128 mole of $NaCl$ react to give $\frac{0.128}{2}=0.064$ mole of $Cl_2$

Now we have to calculate the mass of $Cl_2$

$\text{ Mass of }Cl_2=\text{ Moles of }Cl_2\times \text{ Molar mass of }Cl_2$

$\text{ Mass of }Cl_2=(0.064moles)\times (70.90g/mole)=4.54g$

Therefore, the mass of chlorine gas given off are 4.54 grams.

Answer 2

M(NaCl)/{2M(NaCl)}=m(Cl₂)/M(Cl₂)

m(Cl₂)=M(Cl₂)m(NaCl)/{2M(NaCl)}

m(Cl₂)=70.90*7.5/{2*58.44}=4.55 g

m(Cl₂)=4.55 g