Question

You are working in the laboratory preparing sodium chloride. Consider the following results for three preparations of the compound:
Case 1: $\mathbf{39}\mathbf{.}\mathbf{34}\mathbf{}\mathbf{g}\mathbf{}\mathbf{Na}\mathbf{+}\mathbf{60}\mathbf{.}\mathbf{66}\mathbf{}\mathbf{g}\mathbf{}{\mathbf{Cl}}_2\to \mathbf{100}\mathbf{.}\mathbf{00}\mathbf{}\mathbf{g}\mathbf{}\mathbf{NaCl}$
Case 2: $\mathbf{39}\mathbf{.}\mathbf{34}\mathbf{}\mathbf{g}\mathbf{}\mathbf{Na}\mathbf{+}\mathbf{70}\mathbf{.}\mathbf{00}\mathbf{}\mathbf{g}\mathbf{}{\mathbf{Cl}}_2\to \mathbf{100}\mathbf{.}\mathbf{00}\mathbf{}\mathbf{g}\mathbf{}\mathbf{NaCl}\mathbf{+}\mathbf{9}\mathbf{.}\mathbf{34}\mathbf{}\mathbf{g}\mathbf{}{\mathbf{Cl}}_2$
Case 3: $\mathbf{50}\mathbf{.}\mathbf{00}\mathbf{}\mathbf{g}\mathbf{}\mathbf{Na}\mathbf{+}\mathbf{50}\mathbf{.}\mathbf{00}\mathbf{}\mathbf{g}\mathbf{}{\mathbf{Cl}}_2\to \mathbf{82}\mathbf{.}\mathbf{43}\mathbf{}\mathbf{g}\mathbf{}\mathbf{NaCl}\mathbf{+}\mathbf{17}\mathbf{.}\mathbf{57}\mathbf{}\mathbf{g}\mathbf{}\mathbf{Na}$
Explain these results in terms of the laws of conservation of mass and definite composition.

Short answer

Because the sum of the masses of all reactants equals the sum of the masses of all products, the law of mass holds true.

We may also use this as an example of the law of definite composition because Na and Cl always react in the same proportion of weight.

Step-by-step solution

Step 1:Laws definition

Laws of conservation of mass: ”the mass cannot be generated or destroyed, but can only be converted from one form to another.”

Law of Definite Composition: “the constituents of a pure compound are always mixed in set weight proportions.”

Step 2: Explanation

The law of conservation of massholdstrue because the sum of the masses ofall reactants equals the sum of the masses of all products.

We can also regard this as anillustration of the law of definite composition, as Na and Cl react in the same proportion in all circumstances.

As we can see from the ratio of weight reacted,

$$\begin{gathered} \mathbf{39}\mathbf{.}\mathbf{34}\mathbf{}\mathbf{g}\mathbf{}\mathbf{Na}\mathbf{+}\mathbf{60}\mathbf{.}\mathbf{66}\mathbf{}\mathbf{g}\mathbf{}{\mathbf{Cl}}_{\mathbf{2}}\mathbf{\to }\mathbf{100}\mathbf{.}\mathbf{00}\mathbf{}\mathbf{g}\mathbf{}\mathbf{NaCl} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\frac{\mathbf{Na}\mathbf{}\mathbf{reacted}}{\mathbf{Cl}\mathbf{}\mathbf{reacted}}\mathbf{=}\frac{\mathbf{39}\mathbf{.}\mathbf{34}\mathbf{}\mathbf{g}}{\mathbf{60}\mathbf{.}\mathbf{66}\mathbf{}\mathbf{g}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{648} \end{gathered}$$

$$\begin{gathered} \mathbf{39}\mathbf{.}\mathbf{34}\mathbf{}\mathbf{g}\mathbf{}\mathbf{Na}\mathbf{+}\mathbf{70}\mathbf{.}\mathbf{00}\mathbf{}\mathbf{g}\mathbf{}{\mathbf{Cl}}_2\mathbf{\to }\mathbf{100}\mathbf{.}\mathbf{00}\mathbf{}\mathbf{g}\mathbf{}\mathbf{NaCl}\mathbf{+}\mathbf{9}\mathbf{.}\mathbf{34}\mathbf{}\mathbf{g}\mathbf{}{\mathbf{Cl}}_{\mathbf{2}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\frac{\mathbf{Na}\mathbf{}\mathbf{reacted}}{\mathbf{Cl}\mathbf{}\mathbf{reacted}}\mathbf{=}\frac{\mathbf{39}\mathbf{.}\mathbf{34}\mathbf{}\mathbf{g}}{\mathbf{(}\mathbf{70}\mathbf{.}\mathbf{00}\mathbf{-}\mathbf{9}\mathbf{.}\mathbf{34}\mathbf{)}\mathbf{}\mathbf{g}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{648} \end{gathered}$$

$$\begin{gathered} \mathbf{50}\mathbf{.}\mathbf{00}\mathbf{}\mathbf{g}\mathbf{}\mathbf{Na}\mathbf{+}\mathbf{50}\mathbf{.}\mathbf{00}\mathbf{}\mathbf{g}\mathbf{}{\mathbf{Cl}}_2\mathbf{\to }\mathbf{82}\mathbf{.}\mathbf{43}\mathbf{}\mathbf{g}\mathbf{}\mathbf{NaCl}\mathbf{+}\mathbf{17}\mathbf{.}\mathbf{57}\mathbf{}\mathbf{g}\mathbf{}\mathbf{Na} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\frac{\mathbf{Na}\mathbf{}\mathbf{reacted}}{\mathbf{Cl}\mathbf{}\mathbf{reacted}}\mathbf{=}\frac{\mathbf{(}\mathbf{50}\mathbf{.}\mathbf{00}\mathbf{-}\mathbf{17}\mathbf{.}\mathbf{57}\mathbf{)}\mathbf{}\mathbf{g}}{\mathbf{50}\mathbf{.}\mathbf{00}\mathbf{}\mathbf{g}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{648} \end{gathered}$$

That it is the same in all the three reactions so these reactions also prove the law of definite composition to be true.