2. calculate the atomic mass of each of the following elements using your method from above. test your…

2. calculate the atomic mass of each of the following elements using your method from above. test your answer using the natures mix of isotopes and the periodic table. keep going until you can get two in a row right.\n| element | isotope 1 | | isotope 2 | | isotope 3 | | calculated average atomic mass (amu) | check answer with sim | |\n| ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- |\n| | mass (amu) | %age | mass (amu) | %age | mass (amu) | %age | | yes | no |\n| hydrogen | 1.007 | 99.98 | 2.01410 | 0.011 | - | - | | | |\n| silicon | 27.97 | 92.22 | 28.9764 | 4.685 | 29.97377 | 3.092 | | | |\n| nitrogen | 14.00 | 99.63 | 15.0001 | 0.364 | - | - | | | |\n| argon | 35.96 | 0.336 | 37.9627 | 0.063 | 39.96238 | 99.60 | | | |\ncalculations / rough work:
Answer
Explanation:
Step1: Recall atomic - mass formula
The average atomic mass of an element with isotopes is calculated as $m=\sum_{i = 1}^{n}m_i\times p_i$, where $m_i$ is the mass of the $i$-th isotope and $p_i$ is the percentage abundance of the $i$-th isotope (expressed as a decimal).
Step2: Calculate for Hydrogen
For hydrogen, $p_1 = 0.9998$, $m_1=1.007$, $p_2 = 0.00011$, $m_2 = 2.01410$. $m=(1.007\times0.9998)+(2.01410\times0.00011)$ $m = 1.007\times0.9998+2.01410\times0.00011=1.0068+0.000221551 = 1.007021551\approx1.007$ amu.
Step3: Calculate for Silicon
$p_1 = 0.9222$, $m_1 = 27.97$, $p_2=0.04685$, $m_2 = 28.9764$, $p_3 = 0.03092$, $m_3=29.97377$. $m=(27.97\times0.9222)+(28.9764\times0.04685)+(29.97377\times0.03092)$ $m = 27.97\times0.9222+28.9764\times0.04685 + 29.97377\times0.03092$ $m=25.894934+1.357545+0.926799=28.179278\approx28.18$ amu.
Step4: Calculate for Nitrogen
$p_1 = 0.9963$, $m_1 = 14.00$, $p_2=0.00364$, $m_2 = 15.0001$. $m=(14.00\times0.9963)+(15.0001\times0.00364)$ $m = 14.00\times0.9963+15.0001\times0.00364=13.9482+0.054600364 = 14.002800364\approx14.00$ amu.
Step5: Calculate for Argon
$p_1 = 0.00336$, $m_1 = 35.96$, $p_2=0.00063$, $m_2 = 37.9627$, $p_3 = 0.9960$, $m_3=39.96238$. $m=(35.96\times0.00336)+(37.9627\times0.00063)+(39.96238\times0.9960)$ $m=0.1208256+0.023916501+39.80253048=39.947272587\approx39.95$ amu.
Answer:
| Element | Calculated average atomic mass (amu) |
|---|---|
| Hydrogen | 1.007 |
| Silicon | 28.18 |
| Nitrogen | 14.00 |
| Argon | 39.95 |