Question

1. hydrogen is 99% ¹h, 0.8% ²h, and 0.2% ³h. calculate its average atomic mass.
2. calculate the average atomic mass of magnesium using the following data for three magnesium isotopes.

isotope mass (u) relative abundance
mg - 24 23.985 78.70%
mg - 25 24.986 10.13%
mg - 26 25.983 11.17%

1. calculate the average atomic mass of iridium using the following data for two iridium isotopes.

isotope mass (u) relative abundance
ir - 191 191.0 37.58%
ir - 193 193.0 62.42%

1. lithium has two naturally occurring isotopes: lithium - 6 and lithium - 7. if the average atomic mass of lithium is 6.941 amu, which isotope is the most abundant? how do you know?

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 its relative - abundance (in decimal form).

Step2: Calculate average atomic mass of hydrogen

The mass of $^1H$ is approximately 1 u, $^2H$ is approximately 2 u, and $^3H$ is approximately 3 u.
The relative - abundances in decimal form are: for $^1H$, $p_1 = 0.99$; for $^2H$, $p_2=0.008$; for $^3H$, $p_3 = 0.002$.
The average atomic mass of hydrogen $A_{H}=(1\times0.99)+(2\times0.008)+(3\times0.002)$
$A_{H}=0.99 + 0.016+0.006$
$A_{H}=1.012$ u

Step3: Calculate average atomic mass of magnesium

For $Mg - 24$: $m_1 = 23.985$ u, $p_1=0.7870$
For $Mg - 25$: $m_2 = 24.986$ u, $p_2 = 0.1013$
For $Mg - 26$: $m_3 = 25.983$ u, $p_3=0.1117$
$A_{Mg}=(23.985\times0.7870)+(24.986\times0.1013)+(25.983\times0.1117)$
$A_{Mg}=18.8762+2.5311+2.8923$
$A_{Mg}=24.2996\approx24.30$ u

Step4: Calculate average atomic mass of iridium

For $Ir - 191$: $m_1 = 191.0$ u, $p_1 = 0.3758$
For $Ir - 193$: $m_2 = 193.0$ u, $p_2=0.6242$
$A_{Ir}=(191.0\times0.3758)+(193.0\times0.6242)$
$A_{Ir}=71.7778+120.4706$
$A_{Ir}=192.2484\approx192.25$ u

Step5: Determine the most abundant lithium isotope

Let the abundance of $Li - 6$ be $x$, then the abundance of $Li - 7$ is $1 - x$.
The average atomic mass formula gives $6.941=6x + 7(1 - x)$
$6.941=6x+7 - 7x$
$6.941=7 - x$
$x = 7 - 6.941=0.059$
The abundance of $Li - 6$ is $0.059$ or $5.9\%$ and the abundance of $Li - 7$ is $1 - 0.059 = 0.941$ or $94.1\%$. So, $Li - 7$ is the most abundant isotope because the average atomic mass of lithium is closer to the mass of $Li - 7$ (7 u) than to the mass of $Li - 6$ (6 u).

Answer:

1. Average atomic mass of hydrogen: $1.012$ u
2. Average atomic mass of magnesium: $24.30$ u
3. Average atomic mass of iridium: $192.25$ u
4. The most abundant lithium isotope is $Li - 7$ because its abundance is $94.1\%$ (calculated from the average - atomic - mass formula).