(i) Calculate the total number of electrons present in 1 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 . 6 75 xx 10 ^(-27) g)`
(iii) Find (a) the total number of protons and (b) the total mass of protons in ` 32 mg` of ` NH_3` at ` STP`. ( mass of proton ` = 1 . 6 72 xx 10^(-27) g)`
Will the answer change if the temperature and pressure are changed ?

Explanation

number of electrons prsent in 1 molecule of methane `(CH_(4))`
`{1(6) +4(1)}=10`
number of electrons present in 1 mole i.e `6.023 xx 10^(23) ` molecules of methane
`=6.022 xx10^(23) xx10 =6.022 xx10^(24)`
(ii) (a) number of atoms of `.^(14)C` in 1 mole = `6.023 xx10^(23)`
since 1 atom `.^(14)C` contains (14 – 6) i.e., 8 neutrons, the number of neutrons in ` 14 g` of `^.(14) C` is `( 6.023 xx10^(23) ) xx 8 `, Or
`14 g` of `.^(14)C` contains ` (6.022 xx 10^(23) xx8)` neutrons.
Number of neutrons in 7 mg
`(6.022xx10^(23)xx8xx7mg)/(1400 mg)`
` 2.4092 xx10^(21) `
(b) Mass of one neutron `=1.67493 xx10^(-27)kg`
Mass of total neutrons in` 7g` of `.^(14)C`
`(2.4092 xx 10^(21)) (1.67493 xx10^(-27) kg) `
`4.0352 xx 10^(-6)kg `
(iii) (a) 1 mole of ` NH_(3) ={1(14) +3(1) } g of NH_(3) `
` 17 g` of `NH_(3) `
`6.022 xx10^(23) "molecules" of NH_(3)`
Total number of protons present in 1 molecules of `NH_(3)`
`{1(7) +3(1)}`
10
Number of protons in ` 6.023xx10^(23)` molecules of `NH_(3)`
`(6.023xx10^(23) ) (10)`
`6.023xx10^(24)`
`Rightarrow 17 g of NH_(3) "contains" (6.023 xx10^(24)) ` protons.
Number of protons in 34 mg of `NH_(3)`
`( 6.022 xx10^(24)xx34 mg)/(17000 mg)`
`1.2046 xx 10^(22)`
(b) Mass of one proton `= 1.67493 xx 10^(-27) kg`
Total mass of protons in 34 mg of `NH_(3)`
`( 1.67493 xx 10^(27) kg) (1.2046 xx 10^(22)`
`2.0176xx10^(-5) kg`
The number of protons, electrons, and neutrons in an atom is independent of temperature and pressure conditions. Hence, the obtained values will remain unchanged if the temperature and pressure is changed.