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QuestionFind the number of nanomoles (nmol)(\mathrm{nmol}) in a 79.0 microgram (μg)(\mu \mathrm{g}) gold sample. Round to 3 sig figs.

Studdy Solution

STEP 1

Assumptions1. The sample weight of gold is79.0 micrograms (μg)(\mu \mathrm{g}). . The molar mass of gold (Au) is197.0 g/mol. 3.1 gram (g) = 10610^6 micrograms (μg)(\mu \mathrm{g}). 4.1 mole (mol) = 10910^9 nanomoles (nmol)(\mathrm{nmol}).

STEP 2

First, we need to convert the weight of the gold sample from micrograms (μg)(\mu \mathrm{g}) to grams (g) using the conversion factor1 gram (g) = 10610^6 micrograms (μg)(\mu \mathrm{g}).
Weightg=Weightμg/106Weight_{g} = Weight_{\mu g} /10^6

STEP 3

Now, plug in the given weight of the gold sample in micrograms to calculate the weight in grams.
Weightg=79.0 μg/106Weight_{g} =79.0 \, \mu \mathrm{g} /10^6

STEP 4

Calculate the weight of the gold sample in grams.
Weightg=79.0×10−6 gWeight_{g} =79.0 \times10^{-6} \, \mathrm{g}

STEP 5

Next, we need to convert the weight of the gold sample from grams (g) to moles (mol) using the molar mass of gold, which is197.0 g/mol.
Moles=Weightg/Molar massMoles = Weight_{g} / Molar\, mass

STEP 6

Now, plug in the values for the weight in grams and the molar mass of gold to calculate the number of moles.
Moles=79.0×10−6 g/197.0 g/molMoles =79.0 \times10^{-6} \, \mathrm{g} /197.0 \, \mathrm{g/mol}

STEP 7

Calculate the number of moles of the gold sample.
Moles=79.0×10−6/197.0=4.01×10−7 molMoles =79.0 \times10^{-6} /197.0 =4.01 \times10^{-7} \, \mathrm{mol}

STEP 8

Finally, we need to convert the number of moles to nanomoles (nmol)(\mathrm{nmol}) using the conversion factor1 mole (mol) = 10^ nanomoles (nmol)(\mathrm{nmol}).
anomoles = Moles \times10^

STEP 9

Now, plug in the calculated number of moles to calculate the number of nanomoles.
anomoles=4.01×−7 mol×9anomoles =4.01 \times^{-7} \, \mathrm{mol} \times^9

STEP 10

Calculate the number of nanomoles of the gold sample.
anomoles=4.01×10−7×109=401 nmolanomoles =4.01 \times10^{-7} \times10^9 =401 \, \mathrm{nmol}The79.0 microgram sample of gold is401 nanomoles.

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