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University of Maine

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Problem 6

You need to calculate the number of $\mathrm{P}_{4}$ molecules that can form from 2.5 $\mathrm{g}$ of $\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2} .$ Draw a road map for solving this and write a Plan, without doing any calculations.

Answer

1. Calculate the molar mass of the molecule.

2. Calculate the number of moles we have $\left(\mathrm{n}=\frac{m}{M r}\right)$

3. Calculate the number of moles of $\mathrm{P}\left(\mathrm{n}(\mathrm{P})=2^{*} \mathrm{n}\left(\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}\right)\right.$

4. Divide it by 4 because there are 4 atoms in a molecule.

5. Multiply the molar mass you get by Avogadro constant $\left(\mathrm{N}=\mathrm{n}^{*} \mathrm{N}_{a}\right)$

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## Discussion

## Video Transcript

in a chemical reaction. You can go from one substance to another using the balanced equation. So the balanced equation describes the ratio of substances in terms of moles. So your first step is toe always right. The balanced equation. Using this, you can convert from one substance to another, looking at things in terms of grams, moles, molecules or atoms. So if you know that you have a certain quantity in mass or grams of an initial substance calcium phosphate, we can use our information what we know about relationships between mass and moles as well as the balanced equation, to find out how many molecules of a product which in this case is P four. So I have an initial substance reacted and a product without writing the balanced equation for this. I know that initially I have grams of see a three p a. For to. The first step is to change that two moles cause their balanced equation always deals with moules, and we do this by dividing by the molar mass of calcium phosphate. Once we have moles of calcium phosphate, we can switch two malls of a new substance. In this case, p four and we do that using the mole ratio from the balanced equation. So we multiply by the moles of P for over the moles of See a three p o for to, and this is called the mole ratio, and it's found in the balanced equation. Once we have moles of P four, we can convert it to molecules because we know the relationship between moles and molecules uses of a God rose number. So we'll multiply by of a God rose number or six 102 times 10 to the 23rd. So these steps allow you to go from one substance to another, and by knowing the relationships between things, we confined different quantities.

## Recommended Questions

How many molecules (or formula units) are in each sample?

\begin{equation}\begin{array}{ll}{\text { a. } 85.26 \mathrm{gCCl}_{4}} & {\text { b. } 55.93 \mathrm{kg} \mathrm{NaHCO}_{3}} \\ {\text { c. } 119.78 \mathrm{gC}_{4} \mathrm{H}_{10}} & {\text { d. } 4.59 \times 10^{5} \mathrm{g} \mathrm{Na}_{3} \mathrm{PO}_{4}}\end{array}\end{equation}

The equation for the reaction of phosphorus and chlorine is $\mathrm{P}_{4}(\mathrm{s})+6 \mathrm{Cl}_{2}(\mathrm{g}) \rightarrow 4 \mathrm{PCl}_{3}(\ell) .$ If you use 8000 molecules of $P_{4}$ in this reaction how many molecules of $\mathrm{Cl}_{2}$ are required to consume the $\mathrm{P}_{4}$ completely?

Have each member of your group select one of the molecules shown below and complete steps a-d. Each member should then present his or her results to the rest of the group, explaining the reasoning used to determine the answers.

$$\mathrm{CS}_{2} \quad \mathrm{NCl}_{3} \quad \mathrm{CF}_{4} \quad \mathrm{CH}_{2} \mathrm{F}_{2}$$

\begin{equation}\begin{array}{l}{\text { a. Draw the Lewis dot structure. }} \\ {\text { b. Determine the molecular geometry and draw it accurately. }} \\ {\text { c. Indicate the polarity of any polar bonds within the structure. }} \\ {\text { d. Classify the molecule as polar or nonpolar. }}\end{array}\end{equation}

Determine the number of moles (of molecules or formula units) in each sample.

\begin{equation}\begin{array}{ll}{\text { a. } 25.5 \mathrm{gNO}_{2}} & {\text { b. } 1.25 \mathrm{kg} \mathrm{CO}_{2}} \\ {\text { c. } 38.2 \mathrm{gKNO}_{3}} & {\text { d. } 155.2 \mathrm{kg} \mathrm{Na}_{2} \mathrm{SO}_{4}}\end{array}\end{equation}

Compute (a) the number of moles and (b) the number of molecules in 1.00 $\mathrm{cm}^{3}$ of an ideal gas at a pressure of 100 $\mathrm{Pa}$ and a temperature of 220 $\mathrm{K}$ .

Determine the mass, in grams, of

(a) $7.34 \mathrm{mol} \mathrm{NO}_{2}$

(b) $4.220 \times 10^{25} \mathrm{O}_{2}$ molecules;

(c) $15.5 \mathrm{mol} \mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}$

(d) $2.25 \times 10^{24}$ molecules of $\mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{OH})_{2}$

Calculate the molar masses of the following atmospheric molecules: $(\mathrm{a}) \mathrm{SO}_{2} ;(\mathrm{b}) \mathrm{O}_{3} ;(\mathrm{c}) \mathrm{CO}_{2} ;(\mathrm{d}) \mathrm{N}_{2} \mathrm{O}_{5}$.

Determine the number of molecules of ethanol

$\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)$ in 47.0 $\mathrm{g}$.

Formula Mass and the Mole Concept for Compounds

How many molecules (or formula units) are in each sample?

$$\begin{array}{lllll}{\text { a. } 85.26 \mathrm{gCCl}_{4}} & {\text { b. } 55.93 \mathrm{kg} \mathrm{NaHCO}_{3}} \\ {\mathrm{c} .119 .78 \mathrm{g} \mathrm{C}_{4} \mathrm{H}_{10}} & {\text { d. } 4.59 \times 10^{5} \mathrm{g} \mathrm{Na}_{3} \mathrm{PO}_{4}}\end{array}$$

(a) What is the number of molecules per cubic meter in air at $20^{\circ} \mathrm{C}$ and at a pressure of 1.0 $\mathrm{atm}\left(=1.01 \times 10^{5} \mathrm{Pa}\right)$ ? (b) What is

the mass of 1.0 $\mathrm{m}^{3}$ of this air? Assume that 75$\%$ of the molecules

are nitrogen $\left(\mathrm{N}_{2}\right)$ and 25$\%$ are oxygen $\left(\mathrm{O}_{2}\right)$ .