Question

part 1
isotopes of the element titanium
most of the isotope data on this site has been obtained from the national nuclear data center. please visit their site for more information.
isotopes with a known natural abundance
mass number natural abundance half - life
46 8.25% stable
47 7.44% stable
48 73.72% stable
49 5.41% stable
50 5.18% stable

1. describe in detail the structure of these five isotopes. in what ways are they similar to and different from each other?
2. show a calculation for the average atomic mass. explain the reasoning behind your calculation. what units should it have?
3. what is the neutron:proton ratio for the lightest isotope?
4. explain why melting point is an intensive, quantitative, and physical property. can melting point be used to identify a substance? why or why not?

Explanation:

Step1: Structure of isotopes

Isotopes of titanium have same number of protons (atomic number of Ti is 22), so they have 22 protons. They differ in number of neutrons. For mass - number 46 isotope, number of neutrons = 46 - 22=24; for 47 - mass number isotope, neutrons = 47 - 22 = 25; for 48 - mass number isotope, neutrons = 48 - 22 = 26; for 49 - mass number isotope, neutrons = 49 - 22 = 27; for 50 - mass number isotope, neutrons = 50 - 22 = 28. They are similar in chemical properties as they have the same electron configuration (due to same number of protons and thus same number of electrons in neutral atoms), but different in physical properties like density due to different masses.

Step2: Calculate average atomic mass

The formula for average atomic mass ($A_{avg}$) is $A_{avg}=\sum_{i} (A_{i}\times P_{i})$, where $A_{i}$ is the mass number of the isotope and $P_{i}$ is its natural - abundance (expressed as a decimal).
$A_{avg}=(46\times0.0825)+(47\times0.0744)+(48\times0.7372)+(49\times0.0541)+(50\times0.0518)$
$A_{avg}=3.795 + 3.4968+35.3856 + 2.6509+2.59$
$A_{avg}=47.9183\approx47.92$ u. The units are atomic mass units (u) because we are calculating the mass of an atom relative to the mass of a carbon - 12 atom.

Step3: Neutron - proton ratio for lightest isotope

The lightest isotope has a mass number of 46. It has 22 protons and 24 neutrons. The neutron - proton ratio is $\frac{24}{22}=\frac{12}{11}\approx1.09$.

Step4: Properties of melting point

Melting point is an intensive property because it does not depend on the amount of the substance. It is quantitative as it is measured with a numerical value. It is a physical property as it involves a physical change (solid to liquid) without changing the chemical composition of the substance. Melting point can be used to identify a substance because each pure substance has a characteristic melting point under a given pressure. If the measured melting point of an unknown substance matches the known melting point of a particular substance, it can be a strong indication of the identity of the substance, although impurities can affect the melting point.

Answer:

1. All isotopes have 22 protons. Number of neutrons vary: 24 for mass - number 46, 25 for 47, 26 for 48, 27 for 49, 28 for 50. Similar in chemical properties, different in physical properties.
2. $A_{avg}=(46\times0.0825)+(47\times0.0744)+(48\times0.7372)+(49\times0.0541)+(50\times0.0518)=47.92$ u. Reason: Using the formula $A_{avg}=\sum_{i} (A_{i}\times P_{i})$. Units are atomic mass units (u).
3. $\frac{12}{11}\approx1.09$
4. Intensive: does not depend on amount. Quantitative: has a numerical value. Physical: involves physical change. Can be used to identify a substance as pure substances have characteristic melting points, but impurities can affect it.