Question

Citric acid is concentrated in citrus fruits and plays a central metabolic role in nearly every animal and plant cell. How many moles of citric acid are in 4.79 quarts of lemon juice (d=1.09 g/mL) that is 6.85% citric acid by mass?

Answer 1

At the first we need to calculate the mass of cictric acid as $m = \omega \rho V$ where $\omega$ is the mass fraction, $\rho$ - density and $V$ - volume of solution (we shall use $1[{\text{qt}}] \approx 946.35[{\text{mL]}}$) thus

$$m = 0.0685 \cdot 1.09[\frac{{\text{g}}}{{{\text{mL}}}}] \cdot 4.79[{\text{qt}}] \approx 0.0685 \cdot 1.09[\frac{{\text{g}}}{{{\text{mL}}}}] \cdot 946.35 \cdot 4.79[{\text{mL}}] = 338.46[{\text{g}}]$$

Now we need to calculate the molar mass of citric acid (whose chemical formula is ${C_6}{H_8}{O_7}$) as the sum of atomic weights (can be found in the periodic table)

$$M = 6{M_C} + 8{M_H} + 7{M_O} \approx 6 \cdot 12.01[\frac{{\text{g}}}{{{\text{mol}}}}] + 8 \cdot 1.008[\frac{{\text{g}}}{{{\text{mol}}}}] + 7 \cdot 16[\frac{{\text{g}}}{{{\text{mol}}}}] \approx 192.124[\frac{{\text{g}}}{{{\text{mol}}}}]$$

Now we can calculate the number of moles

$$\nu = \frac{m}{M} = \frac{{338.46[{\text{g}}]}}{{192.124[\frac{{\text{g}}}{{{\text{mol}}}}]}} \approx 1.76[{\text{mol}}]$$