1.) How many carbon atoms are contained in a 1.500 carat diamond (carbon) if 1 caret =200.0 mg?
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I don't know if I'm doing this right but I tried. Can someone help?
1.500 carat diamond (C) *(200.0 mg/1 caret) ...
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3.) Magnesium has a sensity of 1.74 g/cm^3. How many atoms of magnesium are contained in a volume of 12.0 cm^3?
Because they give the Density & Volume, I found the mass but i'm not sure how to do the rest.
DV=M; (1.74g/cm^3)(12.0cm^3)=20.88g
1.) Here is what I did.
1.500 carat diamond (C) * (200.0 mg C/1 caret diamond C) * (1 g C/ 1,000 mg C) *( 1 mol C / 12.011 g C) * (6.022*10^23 atoms C/ 1 mol C)
Sorry its confusing when you type it
1. What yu have gives you mg C. Convert that to grams, then to mols, then to atoms remembering there are 6.02E23 atoms in 1 mole.
2. You have mass Mg. Convert to mols, then to atoms.
Here are my answers after I figured it out. Are these correct though?
1.) 1.50 *10^25 atoms C
2.) 5.173 *10^23 atoms Mg
1 is no. Post your work and I'll find the error. Follow my steps. I suspect you didn't convert mg to grams.
2. ok
For the first question:
To find the number of carbon atoms in a 1.500 carat diamond, you can use the following steps:
1. Start with the given information: 1.500 carat diamond.
2. Use the conversion factor to convert carats to grams. You're given that 1 carat = 200.0 mg. To convert mg to grams, divide by 1000: 200.0 mg/1000 = 0.200 g.
3. Multiply the carat weight in grams by the conversion factor: 1.500 carat diamond * 0.200 g/carat = 0.300 g.
4. Convert the mass in grams of the diamond into moles of carbon using the molar mass of carbon. Carbon has a molar mass of approximately 12.01 g/mol. So, 0.300 g / 12.01 g/mol = 0.02498... mol.
5. Multiply the number of moles of carbon by Avogadro's number (6.022 x 10^23) to find the number of atoms: 0.02498... mol * 6.022 x 10^23 atoms/mol = 1.504 x 10^22 carbon atoms.
Therefore, there are approximately 1.504 x 10^22 carbon atoms in a 1.500 carat diamond.
For the second question:
To find the number of magnesium atoms in a volume of 12.0 cm^3:
1. Start with the given information: density of magnesium = 1.74 g/cm^3 and volume = 12.0 cm^3.
2. Use the density formula: density = mass/volume. Rearrange the formula to solve for mass: mass = density * volume.
3. Substitute the given values: mass = 1.74 g/cm^3 * 12.0 cm^3 = 20.88 g.
4. Convert the mass in grams of magnesium into moles using the molar mass of magnesium. Magnesium has a molar mass of approximately 24.31 g/mol. So, 20.88 g / 24.31 g/mol = 0.8572... mol.
5. Multiply the number of moles of magnesium by Avogadro's number to find the number of atoms: 0.8572... mol * 6.022 x 10^23 atoms/mol = 5.163 x 10^23 magnesium atoms.
Therefore, there are approximately 5.163 x 10^23 magnesium atoms in a volume of 12.0 cm^3.