Video Transcript
What mass of sodium contains the
same number of moles as 10.0 grams of copper? Give your answer to two decimal
places. The molar mass of sodium is 23
grams per mole, and the molar mass of copper is 63.5 grams per mole.
The mole is the SI unit of amount
of substance. One mole of a substance contains
6.022 times 10 to the 23rd entities of that substance. So one mole of copper atoms is
6.022 times 10 to the 23rd copper atoms. And one mole of sodium atoms is
6.022 times 10 to the 23rd sodium atoms. But even though one mole of each of
these substances contains the same number of entities, they don’t have the same
mass.
The mass of one mole of a substance
is the molar mass. Molar mass is given the unit grams
per mole. We can see that we’ve been given
the molar mass of sodium and copper. In this question, we want to know
what mass of sodium contains the same number of moles as 10.0 grams of copper. We know that a mole of copper has a
mass of 63.5 grams. But in the question, we only have
10 grams of copper. So, to answer the question, we’ll
first need to convert the mass of copper into moles of copper.
The number of moles of sodium will
be the same as the number of moles of copper. Then, we can convert the moles of
sodium into grams of sodium. To perform these conversions, we
can use the equation 𝑛 equals lowercase 𝑚 divided by capital 𝑀. In this equation, 𝑛 represents the
amount in moles, lowercase 𝑚 is the mass in grams, and capital 𝑀 is the molar mass
in grams per mole. We can substitute the mass of
copper and the molar mass of copper into the equation. The gram units will cancel, and
we’ll be left with the unit moles. Performing the calculation gives us
a value of 0.15748 moles.
We now know the number of moles of
copper and the number of moles of sodium. To solve for the mass of sodium, we
can substitute the amount of sodium in moles and the molar mass of sodium into the
equation. We multiply both sides of the
equation by 23 grams per mole. The mole units will cancel, leaving
us with the unit grams. Performing the calculation gives us
a mass of 3.6220 grams.
We have calculated the mass of
sodium. But we need to give our answer to
two decimal places. To two decimal places, we have
determined that the mass of sodium that contains the same number of moles as 10
grams of copper is 3.62 grams.
