Question

experimental data
record your results in table 6.1 or in a copy of the table in your notebook.
table 6.1 atomic mass of vegium

| | mass of each isotope (mg)
procedure step 1 | number of each isotope
procedure step 2 | average mass of each (mg)
procedure step 3 | percent of each (%)
procedure step 4 | relative abundance (decimal)
procedure step 5 | relative weight (mg)
procedure step 6
total in step 7 |

sticks	3.5	30	0.116	25.21 %	0.2521	0.0292
clips	22.1	57	0.387	47.29 %	0.4729	0.1832
q-tips	2.3	32	0.071	26.89 %	0.2689	0.0191
total	27.9	119	0.234	100 %	1	0.2334

cleaning up
place the entire sample of vegium back in the plastic cup. make sure that none of the particles are in the sink or on the floor.

questions for analyses
use what you learned in this experiment to answer the following questions.

1. which of your data in table 6.1 must be measured and which can be calculated?

1. in all except step 3 in table 6.1, the numbers in the “total” column can be obtained by adding the numbers across each row. step 3 is an exception because it does not take into account the fact that there are different numbers of each kind of particle. rather than add across, calculate this number in the same way you calculated the other numbers in row 3.

1. what is the difference between percent and relative abundance?

1. what is the result when you total the individual percentages? the individual relative abundances?

Explanation:

Question 1

To determine which data must be measured and which can be calculated, we analyze each column:

• Measured Data: The "Mass of each isotope (mg)" (Step 1) and "Number of each isotope" (Step 2) are directly measured as they involve physically determining the mass and count of each particle (Sticks, Clips, Q - Tips).
• Calculated Data:
• "Average mass of each (mg)" (Step 3): Calculated by dividing the mass of each isotope (Step 1) by the number of each isotope (Step 2) (e.g., for Sticks: $\frac{3.5}{30}\approx0.117$).
• "Percent of each (%)" (Step 4): Calculated by dividing the number of each isotope by the total number of isotopes and multiplying by 100 (e.g., for Sticks: $\frac{30}{119}\times100\approx25.21\%$).
• "Relative abundance (decimal)" (Step 5): Calculated by dividing the number of each isotope by the total number of isotopes (e.g., for Sticks: $\frac{30}{119}\approx0.2521$).
• "Relative weight (mg)" (Step 6): Calculated by multiplying the average mass of each (Step 3) by the relative abundance (Step 5) (e.g., for Sticks: $0.117\times0.2521\approx0.0295$).
• "Total" row values (except Step 3 initially, but Step 3 total is also calculated later): For non - Step 3, they are sums of the respective rows. For Step 3 total, it's calculated as the sum of (average mass × relative abundance) for each isotope.

Step 1: Recall the formula for average mass and relative weight

The average mass of each isotope ($m_i$) is calculated as $m_i=\frac{\text{Mass of isotope }i}{\text{Number of isotope }i}$, and the relative weight ($w_i$) is $w_i = m_i\times\text{Relative abundance of }i$. The total average mass (Step 3 total) should be the sum of the relative weights of each isotope.

Step 2: Calculate the relative weight for each isotope

• For Sticks: $m_{sticks}=0.117$ mg, relative abundance $r_{sticks}=0.2521$, so $w_{sticks}=0.117\times0.2521\approx0.0295$ mg.
• For Clips: $m_{clips}=0.387$ mg, relative abundance $r_{clips}=0.4790$, so $w_{clips}=0.387\times0.4790\approx0.1854$ mg.
• For Q - Tips: $m_{q - tips}=0.071$ mg, relative abundance $r_{q - tips}=0.2689$, so $w_{q - tips}=0.071\times0.2689\approx0.0191$ mg.

Step 3: Sum the relative weights

Sum = $0.0295 + 0.1854+0.0191 = 0.234$ mg.

• Percent Abundance: It is the proportion of a particular isotope in a sample, expressed as a percentage. Mathematically, for an isotope $i$, percent abundance $P_i=\frac{\text{Number of isotope }i}{\text{Total number of isotopes}}\times100$. It represents the fraction of the total number of particles that are of a particular type, multiplied by 100 to get a percentage.
• Relative Abundance: It is the proportion of a particular isotope in a sample, expressed as a decimal. Mathematically, for an isotope $i$, relative abundance $R_i=\frac{\text{Number of isotope }i}{\text{Total number of isotopes}}$. It is the fraction of the total number of particles that are of a particular type, without the multiplication by 100. So, percent abundance is relative abundance multiplied by 100.

Answer:

• Measured: "Mass of each isotope (mg)" (Step 1), "Number of each isotope" (Step 2).
• Calculated: "Average mass of each (mg)" (Step 3), "Percent of each (%)" (Step 4), "Relative abundance (decimal)" (Step 5), "Relative weight (mg)" (Step 6), "Total" row values (including Step 3 total when calculated properly).

Question 2