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Vladimir79
2 months ago
11

A sample of CaCO3 (molar mass 100. g) was reported as being 30. percent Ca. Assuming no calcium was present in any impurities, c

alculate the percent of CaCO3 in the sample.
Chemistry
1 answer:
Anarel [2.9K]2 months ago
3 0

Answer:

About 75%.

Explanation:

Refer to the atomic mass of Ca on a current periodic table:

  • Ca: 40.078.

A mole of Ca atoms is present in each mole of the CaCO₃ compound.

  • The molar mass of one mole of CaCO₃ corresponds to the mass of that compound: \rm 100\; g.
  • The mass of one mole of Ca atoms matches numerically with the relative atomic mass of this element: \rm 40.078\; g.

Determine the mass ratio of Ca within a pure CaCO₃ sample:

\displaystyle \frac{m(\mathrm{Ca})}{m\left(\mathrm{CaCO_3}\right)} = \frac{40.078}{100} \approx \frac{2}{5}.

Assume the mass of the sample is 100 g. This CaCO₃ sample is comprised of 30% Ca by mass. In that 100 grams, there would be \rm 30 \% \times 100\; g = 30\; g Ca atoms. Assuming that there are no Ca impurities. Effectively, all of these Ca atoms are part of CaCO₃. Utilize the ratio \displaystyle \frac{m(\mathrm{Ca})}{m\left(\mathrm{CaCO_3}\right)} \approx \frac{2}{5}:

\begin{aligned} m\left(\mathrm{CaCO_3}\right) &= m(\mathrm{Ca})\left/\frac{m(\mathrm{Ca})}{m\left(\mathrm{CaCO_3}\right)}\right. \cr &\approx 30\; \rm g \left/ \frac{2}{5}\right. \cr &= 75\; \rm g \end{aligned}.

Thus, according to these assumptions, 100 grams of this sample would consist of 75 grams of CaCO₃. Consequently, the percentage mass of CaCO₃ in this sample would be:

\displaystyle 100\%\times \frac{m\left(\mathrm{CaCO_3}\right)}{m(\text{sample})} = \frac{75}{100} = 75\%.

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R represents the gas constant (0.082 atm·L/mol·K)

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I hope this is useful!

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