(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 14C. (Assume that mass of a neutron = 1.675 × 10–27 kg). (iii) Find (a) the total number and (b) the total mass of protons in 34 mg of NH3 at STP. Will the answer change if the temperature and pressure are changed ?
(i) Methane has the chemical formula CH4. The molar mass of methane can b calculated as :
Molar mass of CH4 = Atomic mass of C + 4 × Atomic mass of H
= 12.0111g/mol + (4 )× 1.008 g/mol
= 16.043 g/mol
Therefore, one mole of methane contains 6.022 × 10^23 molecules and hence, it contains 6.022 × 10^23 electrons.
(ii) (a) The atomic mass of 14C is 14. The number of neutrons in 14C can be calculated by subtracting the atomic number (which is 6 for carbon) from the atomic mass:
no of neutrons = (At mass) - (At number)
= 14 - 6
= 8
Therefore, 7 mg of 14C contains (8/14) × (6.022 × 10^23) neutrons = 2.441 × 10^23 neutrons.
(ii) (b) Mass of one neutron is given as 1.675 × 10^-27 kg. Therefore, the total mass of neutrons in 7 mg of 14C can be calculated as:
Total mass of neutrons = Mass of one neutron × Number of neutrons
= 1.675 × 10^-27 kg/neutron × 2.441 × 10^23 neutrons
= 4.086 × 10^-4 kg
Therefore, the total mass of neutrons in 7 mg of 14C is 4.086 × 10^-4 kg.
(iii) (a) The chemical formula of ammonia is NH3. The molar mass of NH3 can b calculated as :
Molar mass of NH3 = Atomic mass of N + 3 × Atomic mass of H
= 14.007 g/mol + 3 × 1.008 g/mol
= 17.031 g/mol
Therefore, one mole of NH3 contains 6.022 × 10^23 molecules and hence, it contains 4 × 6.022 × 10^23 = 2.409 × 10^24 protons.
(iii) (b) Mass of one proton is approximately equal to 1.0073 u or 1.673 × 10^-27 kg. Therefore, the total mass of protons in 34 mg of NH3 can be calculated as:
Total mass of protons = Mass of one proton × Number of protons
= 1.673 × 10^-27 kg/proton × 2.409 × 10^24 protons
= 4.032 × 10^-3 kg
Therefore, the total mass of protons in 34 mg of NH3 is 4.032 × 10^-3 kg.
The number of protons or neutrons in a given mass of a substance does not change with a change in temperature and pressure, as long as the chemical nature of the substance remains the same. Therefore, the answers to parts (ii) and (iii) will not change with a change in temperature and pressure, as long as the substances involved are kept under the same conditions.
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