(i) Calculate the total number of electrons present in one mole of methane.
(ii) Find (a) the total number and (b) the total mass of neutrons in `7 mg " of " ""^(14)C`. (Assume that mass of a neutron = `1.675 xx 10^(-27) kg)`.
(iii) Find (a) the total number and (b) the total mass of protons in `34 kg` of `NH_3` at STP.
Will the answer change if the temperature and pressure are changed?

Explanation

(i) 1 molecule of methane `(CH_4)` contains electrons
`= 6 + 4 = 10`
1 mole or `6.022 xx 10^(23)` molecules of `CH_4` will contain electrons = `6.022 xx 10^(23) xx 10`
`= 6.022 xx 10^(24)`
(ii) In `""^(24)C`
No. of neutrons + No. of Protons = 14
No. of protons = 6
`:.` No of neutrons + 6 = 14
`:.` No. of neutrons = `14 - 6 = 8`
Now `" " 1 mol " of " ""^(14)C = 14 g C`
Or `" " = 6.022 xx 10^(23) "atoms of " ""^(14)C`.
`= 6.022 xx 10^(23) xx 8` neutrons
`= 4.8176 xx 10^(24)` neutrons
(a) 14 g of `""^(14)C` contain = `4.8176 xx 10^(24)` neutrons
`7 mg (7 xx 10^(-3)g)` of `""^(14)C` contain
`= (4.8176 xx 10^(24))/(14) xx 7 xx 10^(-3)` neutrons
`=2.4088 xx 10^(21)` neutrons
(b) Mass of 1 neutron = `1.675 xx 10^(-27) kg`
`:. " Mass of " 2.4088 xx 10^(21)` neutrons
`= 1.675 xx 10^(-27) xx 2.4088 xx 10^(21) kg`
`= 4.035 xx 10^(-6) kg`.
(iii) 1 mole of `NH_3 = 17g NH_3 = 6.022 xx 10^(23)` molecules of `NH_3`
1 molecules of `NH_3` contains protons = `7 + 3 = 10`
(a) 17 g of `NH_3` contain molecule = `6.022 xx 10^(23)`
34 mg of `NH_3` contain molecules
`= (6.022 xx 10^(23))/(17) xx 34 xx 10^(-3)`
`=1.2044 xx 10^(21)`
No. of protons in `34 mg NH_3 = 1.204 xx 10^(21) xx 10`
`= 1.204 xx 10^(22)`
(b) Mass of proton = `1.6726 xx 10^(-27)`
`:.` Mass of `1.204 xx 10^(22)` protons
`=1.6726 xx 10^(-27) xx 1.204 xx 10^(22)`
`= 2.0138 xx 10^(-5) kg`
There is no effect of temperature and pressure.