Answer:
[tex]\boxed {\boxed {\sf 0.0769 \ M}}[/tex]
Explanation:
We are asked to find the molarity of an acid given the details of a titration experiment. The formula for titration is as follows:
[tex]M_AV_A= M_B V_B[/tex]
In this formula, M is the molarity of the acid or base and V is the volume of the acid or base. The molarity of the hydrochloric acid (HCl) is unknown and the volume is 25.0 milliliters.
[tex]M_A * 25.0 \ mL = M_BV_B[/tex]
The molarity of the sodium hydroxide (NaOH) is 0.108 molar and the volume is 17.80 milliliters.
[tex]M_A * 25.0 \ mL = 0.108 \ M * 17.80 \ mL[/tex]
We are solving for the molarity of the acid and we must isolate the variable [tex]M_A[/tex]. It is being multiplied by 25.0 milliliters. The inverse operation of multiplication is division, so we divide both sides of the equation by 25.0 mL.
[tex]\frac {M_A * 25.0 \ mL }{25.0 \ mL}= \frac{0.108 \ M * 17.80 \ mL }{25.0 \ mL}[/tex]
[tex]M_A= \frac{0.108 \ M * 17.80 \ mL }{25.0 \ mL}[/tex]
The units of milliliters cancel.
[tex]M_A= \frac{0.108 \ M * 17.80 }{25.0 }[/tex]
[tex]M_A= \frac{1.9224}{25.0 } \ M[/tex]
[tex]M_A= 0.076896 \ M[/tex]
The original measurements have 3 and 4 significant figures. We must round our answer to the least number of sig figs, which is 3. For the number we calculated, that is the ten-thousandth place. The 9 to the right of this place tells us to round the 8 up to a 9.
[tex]M_A \approx 0.0769 \ M[/tex]
The molarity of the hydrochloric acid is 0.0769 Molar.
