QuestionConvert 4.20 grams of $\mathrm{Ca}_{3} \mathrm{~N}_{2}$ to moles.

Studdy Solution

STEP 1

Assumptions1. The given mass of $\mathrm{Ca}_{3} \mathrm{~}_{}$ is4.20 grams. . The molar mass of $\mathrm{Ca}_{3} \mathrm{~}_{}$ is the sum of the molar masses of its constituent elements, which are Calcium (Ca) and Nitrogen (). The molar mass of Calcium is approximately40.08 g/mol and that of Nitrogen is approximately14.01 g/mol.
3. Avogadro's number is $6.022 \times10^{23}$ , which is the number of entities in one mole of any substance.

STEP 2

First, we need to find the molar mass of $\mathrm{Ca}_{} \mathrm{~}_{2}$ . This is done by adding the molar masses of moles of Calcium and2 moles of Nitrogen.
$Molar\, mass\, of\, \mathrm{Ca}_{} \mathrm{~}_{2} = \times Molar\, mass\, of\, Ca +2 \times Molar\, mass\, of\, N$

STEP 3

Now, plug in the given values for the molar masses of Calcium and Nitrogen to calculate the molar mass of $\mathrm{Ca}_{3} \mathrm{~}_{2}$ .
$Molar\, mass\, of\, \mathrm{Ca}_{3} \mathrm{~}_{2} =3 \times40.08\, g/mol +2 \times14.01\, g/mol$

STEP 4

Calculate the molar mass of $\mathrm{Ca}_{3} \mathrm{~}_{2}$ .
$Molar\, mass\, of\, \mathrm{Ca}_{3} \mathrm{~}_{2} =3 \times40.08\, g/mol +2 \times14.01\, g/mol =148.26\, g/mol$

STEP 5

Now that we have the molar mass of $\mathrm{Ca}_{3} \mathrm{~}_{2}$ , we can find the number of moles in the given mass of $\mathrm{Ca}_{3} \mathrm{~}_{2}$ . This is done by dividing the given mass by the molar mass.
$Number\, of\, moles = \frac{Given\, mass}{Molar\, mass}$

STEP 6

Plug in the values for the given mass and the molar mass to calculate the number of moles.
$Number\, of\, moles = \frac{4.20\, g}{148.26\, g/mol}$

STEP 7

Calculate the number of moles.
$Number\, of\, moles = \frac{4.20\, g}{148.26\, g/mol} \approx0.0283\, mol$ So,4.20 grams of $\mathrm{Ca}_{3} \mathrm{~}_{2}$ is approximately0.0283 moles.

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