Question

The molarity of \[{{HCl}}\] in the resulting solution is approximately: ${{25ml \;of \;3 \;M \;HCl}}$ were added to \[{{75\;ml \;of \;0}}{{.05 \;M \;HCl}}\].
(A) \[{{0}}{{.055M}}\]
(B) \[{{0}}{{.35M}}\]
(C) \[{{0}}{{.787M}}\]
(D) \[{{3}}{{.05M}}\]

Answer 1

Hint: First it is expected we calculate the number of moles present in the given volume of substance. Then these same number of moles will also be present when the solutions get mixed together ten, we can find out a new molarity.

Complete step by step answer:
when two solutions of different molarity are mixed into one solution there is a change in number of moles and volume because of which the molarity changes.
First, we find out the number of moles in each different molarity solution, then we will add both the moles as they will be the total moles present in the mixture
Next, we will add both the volume to get a new amount of volume as molarity is inversely proportional to volume.
${{molarity = }}\dfrac{{{{moles}}}}{{{{volume}}\left( {{{litre}}} \right)}}$
Moles in ${{25 ml\; of \;3M \;HCl = molarity \times volume}}\left( {{{ltr}}} \right)$
${{ = 3M \times 0}}{{.025 \;litre}}$
\[{{3M\; HCl\; moles = 0}}{{.075}}\]
${{moles\; in\; 75 ml \;of\; 0}}{{.05M\; HCl = molarity \times volume (litre)}}$
 ${{ = 0}}{{.05M \times 0}}{{.075 litre}}$
${{0}}{{.05M\; HCl \;moles = 0}}{{.00375 \;moles}}$
So, the total amount of moles in the container is the total moles combined together. \[{{total \;moles = 0}}{{.075 + 0}}{{.00375 = 0}}{{.07875\; moles}}\]
${{total\; volume = 0}}{{.075 + 0}}{{.025 = 0}}{{.1litre}}$
\[{{new \;molarity = }}\dfrac{{{{total\; moles}}}}{{{{total \;volume}}}}\]
${{total\; molarity = }}\dfrac{{{{0}}{{.07875}}}}{{{{0}}{{.1}}}}$
${{total\; molarity = 0}}{{.787M}}$

So, the correct answer is Option C.

Additional Information:
There is a huge difference between molarity and molality of the solution. Molarity is the value calculated as the number of moles in a liter of the solution. Molality is the value calculated as the number of moles in a liter of solvent.

Note: When calculating molarity of the solutions we have to pay attention to the units of volume. The volume of the substance should be in litres so it is recommended we convert the volume in liters so that the moles calculated will be in standard moles but if the volume is in milliliters then the calculated moles will be in millimoles.