Q. 9.106 - An Introduction to General, Organic, and Biological Chemistry

Question

How many grams of solute are in each of the following solutions?

a. $0.428 \mathrm{L}$ of a $0.450{\mathrm{MKKO}}_3$ solution

b. $10.5 \mathrm{mL}$ of a $2.50{\mathrm{MAgNO}}_3$ solution

c. $28.4 \mathrm{mL}$ of a  $6.00{\mathrm{MH}}_3{\mathrm{PO}}_4$ solution

Step-by-Step Solution

Answer

Part a) Molarity$\left(M\right)=\frac{\text{ moles of solutes }}{\text{ liter of solution }}$

Part b) density$\left(\mathrm{g}/{\mathrm{cm}}^3\right)=\frac{\text{ mass }\left(\mathrm{g}\right)}{\text{ volume }\left({\mathrm{cm}}^3\right)}$ or$\frac{\text{ mass }\left(\mathrm{g}\right)}{\text{ volume }\left(\mathrm{mL}\right)}$

Part c) Mass percentage of solute $=\frac{\text{ grams of solute }}{\text{ grams of solution }}\times 100\%$

Part a) $$\begin{gathered} \text{ Moles of solutes }=0.450\left(M\right)\times 0.428 \mathrm{L} \\ =0.1926\mathrm{Moles} \end{gathered}$$

Part b) The amount of solute in the given solution is $4.46 {\mathrm{gAgNO}}_3$

Part c) The amount of solute in the given solution is $16.7 {\mathrm{gH}}_3{\mathrm{PO}}_4$

Step 1: Given information

That are given sentences are : (1)

Define Molarity

Step 2: Explanation (1)

Molarity:

The variety of moles of solute according to Iiter of answer is referred to as molarity of the answer. It symbolized by $\mathit{M}$.Molarity of any answer is a ratio of moles of solutes in step with liter of answer. It expressed via way of means of the subsequent formula: 

Molarity $\left(M\right)=\frac{\text{ moles of solutes }}{\text{ liter of solution }}$

Step 3: Given information (2)

That are given sentences are : (2)

Define density: 

Step 4: Explanation (2)

Density:

The density of a substance is same to the ratio of its mass and volume. In fashionable we are able to say the density of a substance is mass according to unit volume. density $\left(\mathrm{g}/{\mathrm{cm}}^3\right)=\frac{\text{ mass }\left(\mathrm{g}\right)}{\text{ volume }\left({\mathrm{cm}}^3\right)}$ or$\frac{\text{ mass }\left(\mathrm{g}\right)}{\text{ volume }\left(\mathrm{mL}\right)}$

Step 5: Given information

That are given sentences are : (3)

Define mass percentage.

Step 6: Explanation (3)

Mass percentage:

Mass percent is awareness expression of solute which can be percent of the mass of the solution. It expressed with the aid of using the subsequent formula. 

$\text{ Mass percentage of solute }=\frac{\text{ grams of solute }}{\text{ grams of solution }}\times 100\%$

Step 7: Given information (a)

That are given equations are : (a)

Calculate the number of moles .

Step 8: Explanation (a)

A. To calculate the quantity of solute with inside the given answer first calculate the quantity of moles as follows: 

Molarity$\left(M\right)=\frac{\text{ moles of solutes }}{\text{ liter of solution }}$

Moles of solutes = Molarity$\left(M\right)\times$liter of solution

Moles of solutes $=0.450\left(M\right)\times 0.428 \mathrm{L}$ $=0.1926$ Moles

Now calculate the amount of solute by their molar mass as follows:

Mass of solute$=$Molar mass $\times$ number of moles

Mass of solute $=138.205 \mathrm{g}{ \mathrm{mol}}^{-1}{ \mathrm{K}}_2{\mathrm{CO}}_3\times 0.1926$Moles

$=26.6 \mathrm{g}{ \mathrm{K}}_2{\mathrm{CO}}_3$

The amount of solute in the given solution is $26.6 \mathrm{g}{ \mathrm{K}}_2{\mathrm{CO}}_3$.

Step 9: Given information (b).

That are given equation are: (b).

First convert mL into L:

Step 10: Explanation (b)

b.

First convert $\mathrm{mL}$ into L:

$$\begin{gathered} 1000 \mathrm{mL}=1.00 \mathrm{L} \\ 10.5\mathrm{mLL}\times \frac{1.00 \mathrm{L}}{1000\mathrm{\mu rL}}=0.0105 \mathrm{L} \end{gathered}$$

First convert $\mathrm{mL}$ into$\mathrm{L}$ :

$$\begin{gathered} 1000 \mathrm{mL}=1.00 \mathrm{L} \\ 10.5\mathrm{phL}\times \frac{1.00 \mathrm{L}}{1000\mathrm{\mu L}}=0.0105 \mathrm{L} \end{gathered}$$

To calculate the amount of solute in the given solution first calculate the number of moles as follows:

Molarity$\left(M\right)=\frac{\text{ moles of solutes }}{\text{ liter of solution }}$

Moles of solutes = Molarity $\left(M\right)\times$ liter of solution

Moles of solutes $=0.02625$ Moles

Step 11: Given information (c)

That are given equations are :(c).

First calculate the number of moles

Step 12: Explanation (c)

C.

First convert $\mathrm{mL}$ into$\mathrm{L}$ :

$$\begin{gathered} 1000 \mathrm{mL}=1.00 \mathrm{L} \\ 28.4\text{ uKL }\times \frac{1.00 \mathrm{L}}{1000\mathrm{yL}}=0.0284 \mathrm{L} \end{gathered}$$

To calculate the amount of solute in the given solution first calculate the number of moles as follows:

Molarity$\left(M\right)=\frac{\text{ moles of solutes }}{\text{ liter of solution }}$

Moles of solutes = Molarity$\left(M\right)\times$liter of solution

Moles of solutes $=6.0\left(M\right)\times 0.0284 \mathrm{L}$

$=0.1704\text{ Moles }$

Now calculate the amount of solute by their molar mass as follows:

Mass of solute = Molar mass$\times$ number of moles

Mass of solute$=98 \mathrm{g}{ \mathrm{mol}}^{-1}{\mathrm{H}}_3{\mathrm{PO}}_4\times 0.1704$ Moles

$=16.7 {\mathrm{gH}}_3{\mathrm{PO}}_4$

The amount of solute in the given solution is $16.7 {\mathrm{gH}}_3{\mathrm{PO}}_4$.