$(a)$ 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: $H=1, O=16, N=14, Ca=40, Na=23$)

(N/A) Molar mass of $H_{2}O_{2} = (2 \times 1) + (2 \times 16) = 34 \, g/mol$. Percentage of oxygen $= (32 / 34) \times 100 = 94.12 \%$.
$(b)$ Molar mass of $N_{2} = 2 \times 14 = 28 \, g/mol$. Number of moles $= 56 \, g / 28 \, g/mol = 2 \, moles$.
$(c)$ Mass of $Ca = \text{moles} \times \text{atomic mass} = 0.50 \times 40 = 20 \, g$.
$(d)(i)$ Number of molecules $= \text{moles} \times N_{A} = 5 \times 6.022 \times 10^{23} = 30.110 \times 10^{23}$ particles.
$(d)(ii)$ Number of atoms $= (\text{given mass} / \text{atomic mass}) \times N_{A} = (92 / 23) \times 6.022 \times 10^{23} = 4 \times 6.022 \times 10^{23} = 24.088 \times 10^{23}$ particles.