To find the molarity of the solution obtained by mixing 750 mL of 0.5 M HCl with 250 mL of 2 M HCl, we can follow these steps:
### Step 1: Calculate the total volume of the mixed solution.
The total volume (V) of the solution after mixing is the sum of the individual volumes:
\[
V = V_1 + V_2 = 750 \, \text{mL} + 250 \, \text{mL} = 1000 \, \text{mL}
\]
### Step 2: Calculate the number of moles of HCl in each solution.
To find the number of moles of HCl in each solution, we can use the formula:
\[
\text{Number of moles} = \text{Molarity} \times \text{Volume (in L)}
\]
For the first solution (0.5 M HCl):
\[
\text{Moles of HCl}_1 = 0.5 \, \text{M} \times 0.750 \, \text{L} = 0.375 \, \text{moles}
\]
For the second solution (2 M HCl):
\[
\text{Moles of HCl}_2 = 2 \, \text{M} \times 0.250 \, \text{L} = 0.500 \, \text{moles}
\]
### Step 3: Calculate the total number of moles of HCl in the mixed solution.
Now we add the moles from both solutions to get the total moles of HCl:
\[
\text{Total moles of HCl} = \text{Moles of HCl}_1 + \text{Moles of HCl}_2 = 0.375 \, \text{moles} + 0.500 \, \text{moles} = 0.875 \, \text{moles}
\]
### Step 4: Calculate the molarity of the mixed solution.
Finally, we can calculate the molarity (M) of the mixed solution using the formula:
\[
\text{Molarity} = \frac{\text{Total moles of solute}}{\text{Total volume of solution (in L)}}
\]
Convert the total volume from mL to L:
\[
\text{Total volume} = 1000 \, \text{mL} = 1 \, \text{L}
\]
Now, substituting the values:
\[
\text{Molarity} = \frac{0.875 \, \text{moles}}{1 \, \text{L}} = 0.875 \, \text{M}
\]
### Final Answer:
The molarity of the solution obtained by mixing the two solutions is **0.875 M**.
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