High School Chemistry : Identifying Unknown Volume

Study concepts, example questions & explanations for High School Chemistry

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Example Questions

Example Question #1 : Identifying Unknown Volume

What volume of 0.5M sulfuric acid is needed to neutralize 50mL of 0.5M potassium hydroxide? 

Possible Answers:

\(\displaystyle 50mL\)

\(\displaystyle 75mL\)

\(\displaystyle 100mL\)

\(\displaystyle 12.5mL\)

\(\displaystyle 25mL\)

Correct answer:

\(\displaystyle 25mL\)

Explanation:

Sulfuic acid is a diprotic acid and will give two hydrogen ions for each molecule of sulfuric acid that is completely dissociated. Potassium hydroxide has only one hyroxide ion per molecule.

\(\displaystyle H_2SO_4\rightleftharpoons 2H^++SO_4^{2-}\)

\(\displaystyle KOH\rightleftharpoons K^++OH^-\)

Both of these compounds are strong, meaning they will dissociate completely in solution (potassium hydroxide is a strong base and sulfuric acid is a strong acid).

\(\displaystyle H_2SO_4+2KOH\rightleftharpoons 2H_2O+K_2SO_4\)

First, we need to find the moles of potassium hydroxide from the given volume and molarity.

\(\displaystyle M=\frac{mol}{L}\rightarrow mol=(M)(L)\)

\(\displaystyle mol=(0.5M)(50mL)=(0.5M)(0.05L)=0.025mol\ KOH\)

Use stoichiometry to find the volume of sulfuric acid needed to react 0.1mol of potassium hydroxide.

\(\displaystyle 0.025mol\ KOH*\frac{1mol\ H_2SO_4}{2mol\ KOH}*\frac{1L}{0.5mol\ H_2SO_4}=0.025L\ H_2SO_4\)

Our final volume of sulfuric acid is 0.025L, or 25mL.

 

Example Question #81 : Acid Base Chemistry

A chemist has a bottle containing a 2M aqueous solution of hydrochloric acid. He needs to create a 50mL solution of hydrochloric acid that has a concentration of 0.5M. What is the volume of 2M hydrochloric acid that he should dilute in order to achieve the desired concentration?

Possible Answers:

\(\displaystyle \small 37.5mL\)

\(\displaystyle \small 1.25mL\)

\(\displaystyle \small 5mL\)

\(\displaystyle \small 12.5mL\)

Correct answer:

\(\displaystyle \small 12.5mL\)

Explanation:

In order to dilute the concentrated acid, we need to find the amount of concentrated acid that will be diluted to 50mL of total solution. We can find the volume of concentrated acid necessary by setting the final volume and concentration equal to the initial concentration and unknown volume.

\(\displaystyle \small M_{1}v_{1} = M_{2}v_{2}\)

The initial concentration is 2M, the final concentration is 0.5M, and the final volume is 50mL

\(\displaystyle \small (2M)v_{1} = (0.5M)(50 mL)\)

\(\displaystyle \small v_{1} = \frac{(0.5M)(50mL)}{2M}=12.5 mL\)

This means that 12.5mL of concentrated acid needs to be diluted to 50mL of solution. This will result in a solution with a concentration of 0.5M.

Example Question #3 : Identifying Unknown Volume

Starting with 30mL of a .005M \(\displaystyle HCl\) solution, how many milliliters of .010M \(\displaystyle NaOH\) solution are needed to titrate it?

Possible Answers:

\(\displaystyle 15mL\)

\(\displaystyle 30mL\)

None of these

\(\displaystyle 45mL\)

\(\displaystyle 10mL\)

Correct answer:

\(\displaystyle 15mL\)

Explanation:

For this question use the following formula: 

\(\displaystyle N_A M_A V_A = N_B M_B V_B\)

\(\displaystyle N_A\) is the number of acidic hydrogens on the acid, \(\displaystyle M_A\) is the molarity of the acid, \(\displaystyle V_A\) is the volume of the acid, \(\displaystyle N_B\) is the number of basic hydroxides on the base, \(\displaystyle M_B\) is the molarity of the base, \(\displaystyle V_B\) is the volume of the base

Rearrange the equation for the volume of the base:

 \(\displaystyle \frac{N_A M_A V_A }{N_B M_B}= V_B\)

Plug in known values and solve.

\(\displaystyle V_B=15mL\)

Example Question #3 : Identifying Unknown Volume

Starting with 50mL of a .015M \(\displaystyle HNO_3\) solution, how many milliliters of .010M \(\displaystyle NaOH\) solution are needed to titrate it?

Possible Answers:

\(\displaystyle 75mL\)

\(\displaystyle 25mL\)

\(\displaystyle 10mL\)

None of these

\(\displaystyle 50mL\)

Correct answer:

\(\displaystyle 75mL\)

Explanation:

For this question use the following formula: 

\(\displaystyle N_A M_A V_A = N_B M_B V_B\)

\(\displaystyle N_A\) is the number of acidic hydrogens on the acid, \(\displaystyle M_A\) is the molarity of the acid, \(\displaystyle V_A\) is the volume of the acid, \(\displaystyle N_B\) is the number of basic hydroxides on the base, \(\displaystyle M_B\) is the molarity of the base, \(\displaystyle V_B\) is the volume of the base

Rearrange the equation for the volume of the base:

 \(\displaystyle \frac{N_A M_A V_A }{N_B M_B}= V_B\)

Plug in known values and solve.

\(\displaystyle V_B=75mL\)

Example Question #14 : Titrations

Starting with 25mL of a .001M \(\displaystyle HNO_3\) solution, how many milliliters of .010M \(\displaystyle Mg(OH)_2\) solution are needed to titrate it?

Possible Answers:

\(\displaystyle 1.25mL\)

None of these

\(\displaystyle 50mL\)

\(\displaystyle 2.5mL\)

\(\displaystyle 25mL\)

Correct answer:

\(\displaystyle 1.25mL\)

Explanation:

For this question use the following formula: 

\(\displaystyle N_A M_A V_A = N_B M_B V_B\)

\(\displaystyle N_A\) is the number of acidic hydrogens on the acid, \(\displaystyle M_A\) is the molarity of the acid, \(\displaystyle V_A\) is the volume of the acid, \(\displaystyle N_B\) is the number of basic hydroxides on the base, \(\displaystyle M_B\) is the molarity of the base, \(\displaystyle V_B\) is the volume of the base

Rearrange the equation for the volume of the base:

 \(\displaystyle \frac{N_A M_A V_A }{N_B M_B}= V_B\)

Plug in known values and solve.

\(\displaystyle V_B=1.25mL\)

Example Question #1 : Identifying Unknown Volume

Starting with 75mL of a .030M \(\displaystyle HNO_3\) solution, how many milliliters of .022M \(\displaystyle NaOH\) solution are needed to titrate it?

Possible Answers:

\(\displaystyle 102mL\)

\(\displaystyle 25mL\)

\(\displaystyle 50mL\)

\(\displaystyle 75mL\)

None of these

Correct answer:

\(\displaystyle 102mL\)

Explanation:

For this question use the following formula: 

\(\displaystyle N_A M_A V_A = N_B M_B V_B\)

\(\displaystyle N_A\) is the number of acidic hydrogens on the acid, \(\displaystyle M_A\) is the molarity of the acid, \(\displaystyle V_A\) is the volume of the acid, \(\displaystyle N_B\) is the number of basic hydroxides on the base, \(\displaystyle M_B\) is the molarity of the base, \(\displaystyle V_B\) is the volume of the base

Rearrange the equation for the volume of the base:

 \(\displaystyle \frac{N_A M_A V_A }{N_B M_B}= V_B\)

Plug in known values and solve.

\(\displaystyle V_B=102mL\)

Example Question #2 : Identifying Unknown Volume

Starting with 12mL of a .015M \(\displaystyle NaOH\) solution, how many milliliters of .000M \(\displaystyle HBr\) solution are needed to titrate it?

Possible Answers:

\(\displaystyle 440mL\)

\(\displaystyle 710mL\)

\(\displaystyle 360mL\)

None of these

\(\displaystyle 540mL\)

Correct answer:

\(\displaystyle 540mL\)

Explanation:

For this question use the following formula: 

\(\displaystyle N_A M_A V_A = N_B M_B V_B\)

\(\displaystyle N_A\) is the number of acidic hydrogens on the acid, \(\displaystyle M_A\) is the molarity of the acid, \(\displaystyle V_A\) is the volume of the acid, \(\displaystyle N_B\) is the number of basic hydroxides on the base, \(\displaystyle M_B\) is the molarity of the base, \(\displaystyle V_B\) is the volume of the base

Rearrange the equation for the volume of the base:

 \(\displaystyle \frac{N_A M_A V_A }{N_B M_B}= V_B\)

Plug in known values and solve.

\(\displaystyle V_B=540mL\)

Example Question #3 : Identifying Unknown Volume

Starting with 50mL of a .015M \(\displaystyle HBr\) solution, how many milliliters of .010M \(\displaystyle KOH\) solution are needed to titrate it?

Possible Answers:

\(\displaystyle 50mL\)

\(\displaystyle 75mL\)

\(\displaystyle 150mL\)

\(\displaystyle 275mL\)

None of these

Correct answer:

\(\displaystyle 75mL\)

Explanation:

For this question use the following formula: 

\(\displaystyle N_A M_A V_A = N_B M_B V_B\)

\(\displaystyle N_A\) is the number of acidic hydrogens on the acid, \(\displaystyle M_A\) is the molarity of the acid, \(\displaystyle V_A\) is the volume of the acid, \(\displaystyle N_B\) is the number of basic hydroxides on the base, \(\displaystyle M_B\) is the molarity of the base, \(\displaystyle V_B\) is the volume of the base

Rearrange the equation for the volume of the base:

 \(\displaystyle \frac{N_A M_A V_A }{N_B M_B}= V_B\)

Plug in known values and solve.

\(\displaystyle V_B=75mL\)

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