Question

calculate the average atomic masses. round all answers to two decimal places.

1. what is the atomic mass of hafnium if, out of every 100 atoms, 5 have a mass of 176, 19 have a mass of 177, 27 have a mass of 178, 14 have a mass of 179, and 35 have a mass of 180.0?
2. iodine is 80% ¹²⁷i, 17% ¹²⁸i, and 3% ¹²⁹i. calculate the average atomic mass of iodine.
3. calculate the average atomic mass of gold with the 50% being gold - 197 and 50% being gold - 198.
4. calculate the average atomic mass of lithium, which occurs as two isotopes that have the following atomic masses and abundances in nature: 6.017 u, 7.30% and 7.018 u, 92.70%.

Explanation:

Step1: Recall average - atomic - mass formula

The formula for average atomic mass is $\sum_{i}(m_i\times p_i)$, where $m_i$ is the mass of the isotope and $p_i$ is the relative abundance of the isotope.

Question 1:

Step1: Calculate relative abundances of hafnium isotopes

The relative abundances of the hafnium isotopes are:
For mass 176: $p_1=\frac{5}{100} = 0.05$
For mass 177: $p_2=\frac{19}{100}=0.19$
For mass 178: $p_3=\frac{27}{100}=0.27$
For mass 179: $p_4=\frac{14}{100}=0.14$
For mass 180: $p_5=\frac{35}{100}=0.35$

Step2: Calculate average atomic mass

$m = 176\times0.05+177\times0.19 + 178\times0.27+179\times0.14+180\times0.35$
$m=8.8 + 33.63+48.06 + 25.06+63$
$m = 178.55$

Question 2:

Step1: Identify masses and abundances of iodine isotopes

The mass of $^{127}I$ is 127, $p_1 = 0.80$; the mass of $^{126}I$ is 126, $p_2=0.17$; the mass of $^{128}I$ is 128, $p_3 = 0.03$

Step2: Calculate average atomic mass

$m=127\times0.80 + 126\times0.17+128\times0.03$
$m = 101.6+21.42 + 3.84$
$m=126.86$

Question 3:

Step1: Identify masses and abundances of gold isotopes

The mass of gold - 197 is 197, $p_1 = 0.50$; the mass of gold - 198 is 198, $p_2=0.50$

Step2: Calculate average atomic mass

$m=197\times0.50+198\times0.50$
$m=(197 + 198)\times0.50$
$m = 197.50$

Question 4:

Step1: Identify masses and abundances of lithium isotopes

The mass of the first lithium isotope $m_1 = 6.017$, $p_1=0.0730$; the mass of the second lithium isotope $m_2 = 7.018$, $p_2=0.9270$

Step2: Calculate average atomic mass

$m=6.017\times0.0730+7.018\times0.9270$
$m = 0.439241+6.495686$
$m=6.934927\approx6.93$

Answer:

1. 178.55
2. 126.86
3. 197.50
4. 6.93