Only three isotopes of magnesium exist on earth. 24 Mg is the most common form at 78.70% natural abundance with a mass of 23.98504 amu, 25 Mg has a 10.13% natural abundance, while 26 Mg has a natural abundance of 11.17% and a mass of 25.98259 amu. What is the mass of the 25 Mg isotope?

Only 3 isotopes of magnesium exist on Earth. We have magnesium 24, which has a natural abundance of 78.70 percent natural abundance, with a mass of 23.98504 atomic mass units. We also have Mnisen 25, which has, 10.13% natural abundance, and finally, magnesium 26, which has a natural abundance of 11.17% and a mass of 25.98259 atomic mass units. Here it says, what is the mass of the magnesium 25 isotope? If we look on the periodic table, we'll see the atomic mass of magnesium overall. So we're gonna have 24 point 31 equals the mass of our first isotope times the fractional abundance. Remember, fractional abundance, you get it by dividing your, percent abundances or natural abundances by a 100. So So that'd be 0.7870, plus the mass of our second isotope, which is x, times its fractional abundance, plus the mass of our 3rd and final isotope, times its fractional abundance. So now what we're going to do is we're going to multiply all our pairs together. Now when we do that, we're gonna get 24.31 equals 18.87622 648 plus 0.1013x plus 2.90 225-5303. Next, we're going to combine together these two numbers, and that's gonna give me, at this point, 24.31 equals 21.778 48178 plus 0.1013 x. Remember, we need to isolate our x variable here. So next, subtract from both sides 21.778 48178. So when we do that, we'll have on one side our 0.1013x equals 2.5 31518217. Finally, we're going to divide both sides here by 0.1013. And when we do that, that's gonna isolate our x variable. This x variable equals the isotopic mass of magnesium 25. So what we get here is 24.99030. And here, it'll be in atomic mass units, and I have it with 5 decimal places because the other atomic mass units also have 5 decimal places.

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1. Matter and Measurements4h 31m
2. Atoms and the Periodic Table5h 23m
3. Ionic Compounds2h 18m
4. Molecular Compounds2h 18m
5. Classification & Balancing of Chemical Reactions3h 17m
6. Chemical Reactions & Quantities2h 27m
7. Energy, Rate and Equilibrium3h 46m
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13. Alkenes, Alkynes, and Aromatic Compounds2h 12m
14. Compounds with Oxygen or Sulfur1h 6m
15. Aldehydes and Ketones1h 1m
16. Carboxylic Acids and Their Derivatives1h 11m
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2. Atoms and the Periodic Table

Atomic Mass (Simplified)

GOB Chemistry

2. Atoms and the Periodic Table

Atomic Mass (Simplified)

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Multiple Choice

Only three isotopes of magnesium exist on earth. ²⁴Mg is the most common form at 78.70% natural abundance with a mass of 23.98504 amu, ²⁵Mg has a 10.13% natural abundance, while ²⁶Mg has a natural abundance of 11.17% and a mass of 25.98259 amu. What is the mass of the ²⁵Mg isotope?

24.76171 amu

24.99030 amu

25.00138 amu

25.38402 amu

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Verified step by step guidance

Understand that the problem is asking for the mass of the 25Mg isotope, given the natural abundances and masses of the other isotopes.

Recall that the average atomic mass of an element is calculated using the formula: \( \text{Average Atomic Mass} = (\text{Fractional Abundance}_1 \times \text{Mass}_1) + (\text{Fractional Abundance}_2 \times \text{Mass}_2) + (\text{Fractional Abundance}_3 \times \text{Mass}_3) \).

Convert the percentage abundances of each isotope into fractional abundances by dividing by 100. For example, 78.70% becomes 0.7870.

Set up the equation for the average atomic mass of magnesium using the given data: \( 0.7870 \times 23.98504 + 0.1013 \times x + 0.1117 \times 25.98259 = \text{Average Atomic Mass} \), where \( x \) is the mass of the 25Mg isotope.

Solve the equation for \( x \) to find the mass of the 25Mg isotope. This involves isolating \( x \) on one side of the equation and calculating its value using algebraic manipulation.