Titanium has 5 isotopes: Ti-46 (8.0%), Ti-47 (7.8%), Ti-48 (73.4%), Ti-49 (5.5%), and Ti-50 (5.3%), what is the average atomic mass of titanium?

Question

Serenity Allen · Accepted Answer

#"47.923 u"#

The concept here is that each titanium isotope will contribute, in proportion to its abundance, to the element's average atomic mass.

The average atomic mass can be expressed mathematically as

#color(blue)("avg. atomic mass" = sum_i ("isotope"_i xx "abundance"_i))#

You are aware that there are five isotopes in your situation, each with a distinct percent abundance.

To calculate the average atomic mass, you can use the decimal abundance of the isotopes, which is simply the percent abundance divided by #100#.

Each isotope's mass number, which represents the quantity of protons and neutrons in its nucleus, provides information about its atomic mass.

These atomic masses are expressed in unified atomic mass units, or #u#, where

#"1 u " = " 1 proton " color(red)("OR") " 1 neutron"#

Thus, titanium's average atomic mass will be

#m_"a" = "46 u" xx 0.08 + "47 u" xx 0.078 + "48 u" xx 0.734 + "49 u" xx 0.055 + "50 u" xx 0.053#

#m_"a" = color(green)("47.923 u")#

Xavier Avery · Answer

undefined The average atomic mass of titanium is found by multiplying the mass of each isotope by its relative abundance (given as a decimal), adding these values together, and calculating the average atomic mass as follows: average atomic mass = (mass of Ti-46 × relative abundance of Ti-46) + (mass of Ti-47 × relative abundance of Ti-47) + (mass of Ti-48 × relative abundance of Ti-48) + (mass of Ti-50 × relative abundance of Ti-50) = (46 × 0.080) + (47 × 0.078) + (48 × 0.734) + (49 × 0.055) + (50 × 0.053) = 3.68 + 3.67 + 35.23 + 2.695 + 2.65 = 47.925.

Mateo Aguilar · Answer

undefined The average atomic mass of titanium can be calculated using the isotopic masses and their respective abundances:

$$
\text{Average Atomic Mass} = (0.080 \times 46) + (0.078 \times 47) + (0.734 \times 48) + (0.055 \times 49) + (0.053 \times 50)
$$

$$
= 3.68 + 3.67 + 35.23 + 2.695 + 2.65 = 47.925 \, \text{amu}
$$