Relative masses of atoms and molecules

i. What do you understand by the term relative atomic mass?

ii. A sample of boron was found to have the following % composition by mass:

`""_5^10B`(18.7%), `""_5^11B`(81.3%)

Calculate a value for the relative atomic mass of boron. Give your answer to 3 significant figures.

i. That is how heavy one atom is compared with another. More specifically, it refers to the weighted average mass of an atom of the element, relative to 1/12th the mass of a carbon-12 atom.

ii. The relative atomic mass of boron = `[("isotopic mass of B-10" xx "its percentage") + ("isotopic mass of B-11" xx "its percentage")]/100 = [(10 xx 18.7 )+ (11 xx 81.3)] /100 =(187 + 894.3) /100 = 1081.3 / 100 = 10.813 "amu"`.

Boron is present in compounds called borates.

i. Use the Ar values below to calculate the relative molecular mass of iron(III) borate, Fe(BO₂)₃. (A_r values: Fe = 55.8, B = 10.8, O = 16.0)

ii. The accurate relative atomic mass of iron, Fe, is 55.8. Explain why the accurate relative atomic mass is not a whole number.

i. The relative molecular mass of `Fe(BO_2)_3 = 55.8 + 3 xx (10.8 + 2 xx 16.0) = 184.2`

ii. the accurate relative atomic mass is not a whole number because they are an average of the masses of different isotopes of an element, as such Fe has several isotopes. Atomic masses, also known as relative atomic masses, are calculated by taking into account the masses of all the different isotopes of an element and their relative abundance.

i. Hafnium forms a peroxide whose formula can be written as HfO₃.2H₂O. Use the A_r values below to calculate the relative molecular mass of hafnium peroxide.

(A_r values: Hf = 178.5, H = 1.0, O = 16.0)

ii. A particular isotope of hafnium has 72 protons and a nucleon number of 180. Write the isotopic symbol for this isotope, showing this information.

i. The relative molecular mass of hafnium peroxide = `178.5 + 3 xx 16 + 2 xx (2 xx 1.0 + 16.0) = 262.5`

ii. `""_72^180Hf`

The mass spectrum of zirconium is shown below.

i. Use the information from this mass spectrum to calculate the relative atomic mass of zirconium. Give your answer to 3 significant figures.

ii. High-resolution mass spectra show accurate relative isotopic masses. What do you understand by the term relative isotopic mass?

i. `A_r = (90 xx 51.5 + 91 xx 11.2 + 92 xx 17.1 + 94 xx 17.4 + 96 xx 2.8) / 100 = 91.318.`

ii. The term relative isotopic mass for the mass of a particular isotope of an element on a scale where an atom of carbon-12 has a mass of exactly 12 units. For example, the relative isotopic mass of carbon-13 is 13.00.

Hydrocarbons are compounds of carbon and hydrogen only. Hydrocarbon Z is composed of 80 % carbon and 20 % hydrogen.

i. Calculate the empirical formula of hydrocarbon Z. (A_r values: C = 12.0, H = 1.0).

ii. The molar mass of hydrocarbon Z is 30.0 g.mol^–1. Deduce the molecular formula of this hydrocarbon.

i. We assume a mass of 100 g of stuff

Moles of Carbon = `80.0 / 12.0 = 6.67 mol`.

Moles of Hydrogen = `20.0 / 1.0 = 20 mol`.

Thus,

`C = 6.67 / 6.67 = 1`

`H = 20 / 6.67  = 3`

So the empitical formula is `CH_3`.

ii. The molar mas of Z = `30 g.mol^(-1) = (12.0 + 3 xx 1.0) xx n => n = 2`

The molecular formula of this hydrocarbon is `C_2H_6`.

Which is the correct definition of relative atomic mass? 

A. the total mass of the subatomic particles in an atom 

B. the mass of an atom compared to 1/12 the mass of a carbon-12 atom 

C. the mass of an atom compared to the mass of a hydrogen-1 atom 

D. the mass of a proton

The answer is B.

Relative atomic mass, Ar, is the mass of one element compared to other. This is compared to carbon-12 as the standard of reference and this is defined as the atomic mass unit (amu) which has value of 1.6606 x 10^-24 g.

A is incorrect as there is no comparison to allow for the term relative atomic mass

C is incorrect because this is the way that relative atomic mass used to be calculated, but because of isotopes and the role of carbon in organic compounds, it was changed to carbon-12.

D is incorrect as the atom will contain neutrons which also have a mass.

Tetraethyl lead, Pb(C₂H₅)₄, has been used as a petrol additive. 

What is the percentage by mass of carbon in tetraethyl lead?

A. 10.2                    

B. 14.9                     

C. 29.7                      

D. 32.0

The answer is C.

Relative formula mass of tetraethyl lead = `207 + ( 2 xx 12.0 + 5 xx 1.0) xx 4 = 323`

So the mass of carbon in this case is `(12.0 xx 2) xx 4  = 96`

The the pecentage by mass of carbon in tetraethyl lead is given by `96/323 xx 100% = 29.7%`.

 What is the relative formula mass of ammonium nitrate, NH₄NO₃? 

A. 80 

B. 108 

C. 122 

D. 150

The answer is A.

The relative formula mass of ammonium nitrate = `2 xx 14.0 + 4 xx 1.0 + 3 xx 16.0 = 80 g.mol^(-1)`

The relative atomic masses of all elements have been found with respect to an atom of ____

A. N-14

B. C-14

C. C-16

D. None of the above.

The answer is D.

The International Union of Chemists selected the most stable carbon isotope (C-12) or ¹²C as the standard for comparison of the atomic masses of various elements. 

The mass of C-12 is taken as a 12 atomic mass unit (standard). 

A Carbon-12 contains six protons, six neutrons, and six electrons.

Which is the correct definition of relative molecular mass, M_r?

A. `"Average mass of one atom" / "1/12 mass of an atom 12C"`

B. `(Σ ("percentage isotope abundance" xx "isotope mass number") )/ 100`

C. `"Average mass of one molecule" / "Mass of an atom of 12C"`

D. `"Average mass of one molecule" / "1/12 mass of an atom of 12C"`

The answer is D.

A is incorrect as this is a definition of relative atomic mass.

B is incorrect because this is the calculation for determining relative isotopic mass.

C is incorrect as this is a common incorrect definition of relative molecular mass.