the atomic mass for each element is reported on the periodic table. this number is a weighted average of the masses of each of the isotopes of an element. for example, the atomic mass of carbon is reported as 12.011 amu. carbon is composed primarily of two isotopes: carbon - 12 and carbon - 13. the atomic mass is calculated from the relative abundance and the masses for these two isotopes. using the equation below we can calculate the atomic mass for carbon.
atomic mass = % isotope 1×mass isotope 1+% isotope 2×mass isotope 2+
carbon - 12 makes up 98.93% of all of the carbon atoms, while carbon - 13 is about 1.07% abundant. since the carbon - 12 isotope is more abundant, its mass is weighted more in the calculation of carbons atomic mass. an example calculation is done below.
example
what is the atomic mass (the weighted average mass) for carbon?
substitute values in equation (convert % to decimals)
atomic mass=(0.9893)×(12.000amu)+(0.0107)×(13.003amu)
calculate
atomic mass = 12.01 amu
use the equation for atomic mass to answer the following questions.
1. argon has three naturally occurring isotopes: argon - 36, argon - 38, and argon - 40. based on argons reported atomic mass, which isotope do you think is the most abundant in nature? explain.
2. copper is made of two isotopes. copper - 63 is 69.17% abundant and it has a mass of 62.9296 amu. copper - 65 is 30.83% abundant and it has a mass of 54.9278 amu. what is the weighted average mass of these two isotopes?
3. calculate the atomic mass of silicon. the three silicon isotopes have atomic masses and relative abundances of 27.9769 amu (92.2297%), 28.9765 amu (4.6832%) and 29.9738 amu (3.0872%).
4. gallium has two naturally occurring isotopes. the mass of gallium - 69 is 68.9256 amu and it is 60.108% abundant. the mass of gallium - 71 is 70.9247 amu and it is 39.892% abundant. find the atomic mass of gallium.
5. bromine has two naturally occurring isotopes. bromine - 79 has a mass of 78.918 amu and is 50.69% abundant. using the atomic mass reported on the periodic table, determine the mass of bromine - 81, the other isotope of bromine.
6. calculate the atomic mass of lead. the four lead isotopes have atomic masses and relative abundances of 203.973 amu (1.4%), 205.974 amu (24.1%), 206.976 amu (22.1%) and 207.977 amu (52.4%).
antimony has two naturally occurring isotopes. the mass of antimony - 121 is 120.904 amu and the mass of antimony - 123 is 122.904 amu. using the average mass from the periodic table, find the abundance of each isotope. (remember that the sum of the two abundances must be 100)

Question

Accepted Answer

1.
# Explanation:
## Step1: Recall atomic - mass concept
The atomic mass is a weighted - average mass of an element's isotopes. The more abundant an isotope, the more it contributes to the atomic mass. Argon's reported atomic mass is approximately 39.95 amu. This value is closest to the mass of argon - 40. So, argon - 40 is the most abundant isotope in nature.
# Answer:
Argon - 40 is the most abundant isotope in nature because the reported atomic mass of argon (approx. 39.95 amu) is closest to the mass of argon - 40.

2.
# Explanation:
## Step1: Use atomic - mass formula
The formula for atomic mass (weighted average mass) is $atomic\ mass=\sum_{i}(\% \ abundance_i	imes mass_i)$. For copper, we have two isotopes. Copper - 63 with $\%$ abundance $= 0.6917$ and mass $= 62.9296$ amu, and copper - 65 with $\%$ abundance $=0.3083$ and mass $=54.9278$ amu.
## Step2: Calculate
$atomic\ mass=(0.6917	imes62.9296)+(0.3083	imes54.9278)$
$=(0.6917	imes62.9296)=43.5286$
$(0.3083	imes54.9278)=16.9342$
$atomic\ mass = 43.5286 + 16.9342=60.4628$ amu
# Answer:
The weighted - average mass of the two copper isotopes is 60.4628 amu.

3.
# Explanation:
## Step1: Apply atomic - mass formula
The formula for atomic mass is $atomic\ mass=\sum_{i}(\% \ abundance_i	imes mass_i)$. For silicon, we have three isotopes:
Isotope 1: $\%$ abundance $=0.922297$, mass $=27.9769$ amu
Isotope 2: $\%$ abundance $=0.046832$, mass $=28.9765$ amu
Isotope 3: $\%$ abundance $=0.030872$, mass $=29.9738$ amu
## Step2: Calculate
$atomic\ mass=(0.922297	imes27.9769)+(0.046832	imes28.9765)+(0.030872	imes29.9738)$
$(0.922297	imes27.9769)=25.7057$
$(0.046832	imes28.9765)=1.3562$
$(0.030872	imes29.9738)=0.9253$
$atomic\ mass=25.7057 + 1.3562+0.9253 = 27.9872$ amu
# Answer:
The atomic mass of silicon is 27.9872 amu.

4.
# Explanation:
## Step1: Use atomic - mass formula
The formula for atomic mass is $atomic\ mass=\sum_{i}(\% \ abundance_i	imes mass_i)$. For gallium, we have two isotopes: gallium - 69 with $\%$ abundance $=0.60108$ and mass $=68.9256$ amu, and gallium - 71 with $\%$ abundance $=0.39892$ and mass $=70.9247$ amu.
## Step2: Calculate
$atomic\ mass=(0.60108	imes68.9256)+(0.39892	imes70.9247)$
$(0.60108	imes68.9256)=41.4097$
$(0.39892	imes70.9247)=28.2047$
$atomic\ mass=41.4097 + 28.2047=69.6144$ amu
# Answer:
The atomic mass of gallium is 69.6144 amu.

5.
# Explanation:
## Step1: Let the mass of bromine - 81 be $x$ amu
The atomic mass of bromine from the periodic table is approximately 79.904 amu. Bromine - 79 has a $\%$ abundance of $0.5069$ and mass $=78.918$ amu, and bromine - 81 has a $\%$ abundance of $1 - 0.5069 = 0.4931$.
## Step2: Set up the atomic - mass equation
$79.904=(0.5069	imes78.918)+(0.4931	imes x)$
$(0.5069	imes78.918)=40.0045$
$79.904 - 40.0045=0.4931x$
$39.8995 = 0.4931x$
$x=\frac{39.8995}{0.4931}=80.916$ amu
# Answer:
The mass of bromine - 81 is 80.916 amu.

6.
# Explanation:
## Step1: Use atomic - mass formula
The formula for atomic mass is $atomic\ mass=\sum_{i}(\% \ abundance_i	imes mass_i)$. For lead, we have four isotopes:
Isotope 1: $\%$ abundance $=0.014$, mass $=203.973$ amu
Isotope 2: $\%$ abundance $=0.241$, mass $=205.974$ amu
Isotope 3: $\%$ abundance $=0.221$, mass $=206.976$ amu
Isotope 4: $\%$ abundance $=0.524$, mass $=207.977$ amu
## Step2: Calculate
$atomic\ mass=(0.014	imes203.973)+(0.241	imes205.974)+(0.221	imes206.976)+(0.524	imes207.977)$
$(0.014	imes203.973)=2.8556$
$(0.241	imes205.974)=49.6497$
$(0.221	imes206.976)=45.7417$
$(0.524	imes207.977)=109.9709$
$atomic\ mass=2.8556 + 49.6497+45.7417+109.9709 = 208.2179$ amu
# Answer:
The atomic mass of lead is 208.2179 amu.

7.
# Explanation:
## Step1: Let the abundance of antimony - 121 be $a$, then the abundance of antimony - 123 is $1 - a$
The average atomic mass of antimony from the periodic table is approximately 121.760 amu.
## Step2: Set up the atomic - mass equation
$121.760=a	imes120.904+(1 - a)	imes122.904$
$121.760 = 120.904a+122.904-122.904a$
$121.760-122.904=(120.904 - 122.904)a$
$- 1.144=-2a$
$a = 0.572$ or $57.2\%$
The abundance of antimony - 123 is $1 - 0.572 = 0.428$ or $42.8\%$
# Answer:
The abundance of antimony - 121 is 57.2% and the abundance of antimony - 123 is 42.8%.

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QUESTION IMAGE

Question

Explanation:

Step1: Recall atomic - mass concept

Step1: Use atomic - mass formula

Step2: Calculate

Step1: Apply atomic - mass formula

Step2: Calculate

Answer: