Question

10 mL of hydrogen gas combined with $5$ mL oxygen to yield water. When $200$ mL of hydrogen gas at NTP is passed over heated CuO, the CuO loses $0.144$ g of its mass. Do these data correspond to the law of constant proportions?

Answer 1

Law of constant proportions states that chemical compounds that are made of individual elements are always present in a fixed proportion by mass. Although the ratio doesn’t depend on the source of the chemical compound or the route through which it has been prepared. So we will equate the weights of hydrogen and oxygen in both cases to see whether the law of constant proportions holds or not.

Complete step by step answer:
We have been given ten mL of hydrogen gas combined with five mL oxygen to yield water. Therefore we calculate the weight of $10$ mL hydrogen at STP.
The reaction is ${H_2} + \dfrac{1}{2}{O_2} \to {H_2}O$
We get
Mass of $10$mL hydrogen at NTP$= \dfrac{{10 \times 2}}{{22400}} = \dfrac{{20}}{{22400}} = 0.000893g$
Therefore, the mass of $10$ mL hydrogen at NTP $= 0.000893g$
Now we calculate the weight of $5$ mL oxygen at STP. We get
Mass of $5$ mL of oxygen at STP$= \dfrac{{5 \times 32}}{{22400}} = 0.000714g$
Therefore, the mass of $5$ mL oxygen at NTP is $0.000714g$
Therefore the ratio of masses of hydrogen and oxygen $= \dfrac{{0.00089}}{{0.000714}} = \dfrac{1}{8}$

Considering the second case we get
We have been given $200$ mL of hydrogen at NTP is passed over heated CuO. We will calculate the mass of $200$ mL of hydrogen at NTP. So we get
Weight of $200$mL of hydrogen at NTP $= \dfrac{{2 \times 200}}{{22400}} = 0.0178g$
Now the mass of oxygen which is lost by CuO which combined with $0.0178$g hydrogen at NTP to form water is $0.144$ g
Therefore the ratio of masses of hydrogen and oxygen $= \dfrac{{0.0178}}{{0.144}} = \dfrac{1}{8}$
Hence the ratio by mass is coming $\dfrac{1}{8}$ which is the same in both the cases.
Hence, the law of constant proportions holds in this case.

Note: This law holds for stoichiometric compounds only. It is because the elements are present in a fixed proportion by mass. The ratio in non-stoichiometric compounds varies from sample to sample and is not fixed and so they don’t follow the law of constant proportions.