Assume that the element 107Uns is synthesized and that the sample contains 39.8% 270Uns (269.4 amu), 35.2% 271Uns (270.3 amu) and 25.0% 272Uns (271.2 amu). What is the value of the atomic weight?
A. 270.
B. 269.3
C. 270.4
D. 271
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So this is what I did, but for some reason, it continues to not turn out. SO i am thinking is it significant figures reason?
here is what i have, please tell me what i am doing wrong and what the answer is?
this is what i did:
(39.8/100) (269.4 amu) + (35.2/100) (270.3 amu) + (25.0/100)(271.2 amu)
And I got 270.1668 amu
But it isn't one of the choices. So I was thinking is it because of significant figures or miscalculation? OR what would the answer be?
It can't be B and the mass is less than the mass of any of the isotopes.
The % values are to three sig figs so might expect the answer to be to 3 sig figs. The only one that fits is A.
If you round each step to 3 sig figs and then add you get 269.9 or 270 to 3 sig figs.
Oh, I see you're in a bit of a pickle with this question! Let's see if we can figure it out together, shall we?
To find the atomic weight, you'll need to calculate the weighted average of the different isotopes. You've already done that correctly, using the given percentages and atomic masses of each isotope. However, it seems like you may have made a rounding error in your calculations.
Let's go through the calculations one more time:
(39.8/100) * 269.4 amu + (35.2/100) * 270.3 amu + (25.0/100) * 271.2 amu
= 0.398 * 269.4 amu + 0.352 * 270.3 amu + 0.25 * 271.2 amu
= 107.2072 amu + 95.3256 amu + 67.8 amu
= 270.3338 amu
Now, when it comes to significant figures, it's always wise to adhere to the least number of decimal places in your data. In this case, the percentage values given have one decimal place, so your final answer should also have one decimal place. Therefore, the correct atomic weight value would be rounded to 270.3 amu.
So, the correct answer would be B. 269.3. Oops, sorry! Just a little clown mistake there. The correct answer is actually 270.3 amu. Keep up the good work and remember, don't clown around with those significant figures!
To calculate the atomic weight, you need to multiply the percent composition of each isotope by its mass and then sum them up. However, it seems like you made a mistake in your calculation.
Here's the correct step-by-step calculation:
1. Convert the percent compositions to decimal form:
39.8% = 0.398
35.2% = 0.352
25.0% = 0.250
2. Multiply the percent compositions by the mass of each isotope:
(0.398)(269.4 amu) = 107.4792 amu
(0.352)(270.3 amu) = 95.0656 amu
(0.250)(271.2 amu) = 67.8000 amu
3. Sum up the calculated values:
107.4792 amu + 95.0656 amu + 67.8000 amu = 270.3448 amu
4. Round the atomic weight to the correct number of significant figures. Since the least precise value given has 3 significant figures (271.2 amu), the final answer should also have 3 significant figures:
Therefore, the rounded atomic weight is 270.
Hence, the correct answer is option A) 270.
To find the atomic weight, we need to determine the weighted average of the masses of the isotopes present in the sample. It seems like you have followed the correct process for calculating the atomic weight, but there might be some rounding errors or significant figures issues in your calculations.
Let's go through the calculation step by step:
1. Convert the percentages to decimal form:
- 39.8% becomes 0.398
- 35.2% becomes 0.352
- 25.0% becomes 0.250
2. Multiply the decimal percentages by the mass of each isotope:
- (0.398)(269.4 amu) = 107.3892 amu
- (0.352)(270.3 amu) = 95.1456 amu
- (0.250)(271.2 amu) = 67.8000 amu
3. Add up the masses of the isotopes:
107.3892 amu + 95.1456 amu + 67.8000 amu = 270.3348 amu
Now, let's consider significant figures. Since the given percentages have three significant figures, the final answer should also have three significant figures. Therefore, the atomic weight, rounded to three significant figures, is 270.
Hence, option A, 270, is the correct answer.