Question

2.2 Chromium has four naturally-occurring isotopes: 4.34% of 50Cr, with an atomic weight of 49.9460 amu; 83.79% of 52Cr, with an atomic weight of 51.9405 amu; 9.50% of 53Cr, with an atomic weight of 52.9407 amu; and 2.37% of 54Cr, with an atomic weight of 53.9389 amu. On the basis of these data, confirm that the average atomic weight of Cr is 51.9963 amu.

Answer 1

To calculate the average atomic weight of chromium, we multiply the mass of each isotope by its abundance and add up the products.

Step-by-step explanation:

When data is available regarding the natural abundance of various isotopes of an element, it is simple to calculate the average atomic mass. In the case of chromium, we have the abundance and mass of four naturally occurring isotopes. To calculate the average atomic weight of chromium, we multiply the mass of each isotope by its abundance, and then add up the products. For example, for the isotope 50Cr with an abundance of 4.34% and a mass of 49.9460 amu, the product is (0.0434 × 49.9460) = 2.17133 amu. We repeat this calculation for the other three isotopes, and then sum up the results. The final result is the average atomic weight of chromium, which in this case is 51.9963 amu.

Answer 2

Average atomic mass = 51.9963 amu

Step-by-step explanation:

Given data:

Abundance of Cr⁵⁰ with atomic mass= 4.34% , 49.9460 amu

Abundance of Cr⁵² with atomic mass = 83.79%, 51.9405 amu

Abundance of Cr⁵³ with atomic mass =9.50%, 52.9407 amu

Abundance of Cr⁵⁴ with atomic mass = 2.37%, 53.9389 amu

Average atomic mass = 51.9963 amu

Solution:

Average atomic mass = (abundance of 1st isotope × its atomic mass) +(abundance of 2nd isotope × its atomic mass +....n) / 100

Average atomic mass = (4.34×49.9460)+(83.79×51.9405) +(9.50×52.9407)+ (2.37×53.9389) / 100

Average atomic mass = 216.7656 + 4352.0945 + 502.9367 +127.8352 / 100

Average atomic mass = 5199.632 / 100

Average atomic mass = 51.9963 amu