Calculate the mass of the following: (i) 0.5 mole of `N_(2)` gas (mass from mole of molecule) (ii) 0.5 mole of N atoms (mass from mole of atom) (iii) `3.011 × 10_(23)` number of N atoms (mass from number) (iv) `6.022 × 10_(23)` number of `N_(2)` molecules (mass from number)
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(i) mass = molar mass × number of moles `⇒ m = M × n = 28 × 0.5 = 14 g` (ii) mass = molar mass × number of moles `⇒ m = M × n = 14 × 0.5 = 7 g` (iii) The number of moles, n = `("given number of particles")/("Avogadro number") = (N)/(N_(0))` `=(3.011xx10^(23))/(6.022xx10^(23))`
`impliesm = M xx n = 14 xx (3.011 xx 10^(23))/(6.022 xx 10^(23))` `=14xx0.5 = 7 g` `n = (N)/(N_(0))` `implies m = M xx (N)/(N_(0))= 28 xx(6.022xx10^(23))/(6.022xx10^(23))` `= 28 xx 1= 28 g`
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