How many mL of 3.00M HNO3 would you need to make exactly 100mL of 0.83 HNO3 by dilution with water? (The FM of HNO3 = 63.0.)
0.83 WHAT.
27.67ml
To solve this problem, we can use the equation for dilution:
\(C_1V_1 = C_2V_2\)
where:
\(C_1\) is the initial concentration of the solution,
\(V_1\) is the initial volume of the solution,
\(C_2\) is the final concentration of the solution, and
\(V_2\) is the final volume of the solution.
In this case, we are given:
\(C_1 = 3.00\) M,
\(V_1\) (unknown),
\(C_2 = 0.83\) M, and
\(V_2 = 100\) mL.
First, let's rearrange the equation:
\(V_1 = \frac{{C_2V_2}}{{C_1}}\)
Now we can substitute the known values and solve for \(V_1\):
\(V_1 = \frac{{0.83 \, \text{M} \times 100 \, \text{mL}}}{{3.00 \, \text{M}}}\)
\(V_1 = \frac{{83 \, \text{mL} \times \text{mol/L} \times \text{mL}}}{3.00 \, \text{mol/L}}\)
Next, let's convert the units from mL to L:
\(V_1 = \frac{{83 \, \text{mL} \times 1 \, \text{L/1000 \, mL}} \times \text{mol/L}}{3.00 \, \text{mol/L}}\)
\(V_1 = \frac{{83 \times 1 \times \text{mol}}}{{3.00 \times 1000}}\)
\(V_1 = \frac{{83}}{{3.00 \times 1000}}\)
Finally, we can calculate the value of \(V_1\) by performing the division:
\(V_1 \approx 0.0277\) L
To convert this to mL, we multiply by 1000:
\(V_1 \approx 27.7\) mL
Therefore, you would need approximately 27.7 mL of 3.00 M HNO3 to make exactly 100 mL of 0.83 M HNO3 by dilution with water.