$A$ sample of ethane $(C_2H_6)$ gas has the same mass as $1.5 \times 10^{20}$ molecules of methane $(CH_4)$. How many $C_2H_6$ molecules does the sample of gas contain?

$(a)$ What is the law of constant proportions? Explain with the help of an example.
$(b)$ Which postulate of Dalton's atomic theory is in agreement with this law?

Which of the following would weigh the highest?

Write the molecular formulae for the following compounds:
$(a)$ Copper $(II)$ bromide
$(b)$ Aluminium $(III)$ nitrate
$(c)$ Calcium $(II)$ phosphate
$(d)$ Iron $(III)$ sulphide
$(e)$ Mercury $(II)$ chloride
$(f)$ Magnesium $(II)$ acetate

$(a)$ Calculate the percentage of oxygen in $H_{2}O_{2}$.
$(b)$ Calculate the number of moles in $56 \, g$ of nitrogen gas $(N_{2})$.
$(c)$ Calculate the mass of $0.50$ moles of $Ca$ atoms.
$(d)$ Find out the number of particles in:
$(i)$ $5$ moles of methane gas $(CH_{4})$
$(ii)$ $92 \, g$ of sodium $(Na)$
(Atomic masses: $H=1, O=16, N=14, Ca=40, Na=23$)

Calculate the mass of $20$ water molecules.