The concentration of citric acid (H3C6H5O7) in citric fruits ranges from 0.005 M to 0.30 M. Consider a 12.6 mL sample of pure lime juice with a citric acid concentration of 0.295 M. How many grams of citric acid are in the sample?
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To determine the number of grams of citric acid in the sample, we need to use the formula:
Grams = moles × molar mass
First, we need to calculate the number of moles of citric acid in the sample. The formula to calculate the number of moles is:
Moles = concentration × volume
Given:
Concentration = 0.295 M
Volume = 12.6 mL
To use this volume in the equation, it is best to convert it to liters. There are 1000 mL in 1 L, so:
Volume = 12.6 mL ÷ 1000 mL/L = 0.0126 L
Plugging in the values:
Moles = 0.295 M × 0.0126 L = 0.003717 moles
Now, we need to find the molar mass of citric acid. The molar mass can be calculated based on the molecular formula. For citric acid (H3C6H5O7):
Molar mass = (3 × molar mass of hydrogen) + (6 × molar mass of carbon) + (5 × molar mass of hydrogen) + (7 × molar mass of oxygen)
The molar mass of hydrogen (H) is approximately 1 g/mol, the molar mass of carbon (C) is approximately 12 g/mol, and the molar mass of oxygen (O) is approximately 16 g/mol.
Plugging in the values:
Molar mass = (3 × 1 g/mol) + (6 × 12 g/mol) + (5 × 1 g/mol) + (7 × 16 g/mol)
Molar mass = 3 g/mol + 72 g/mol + 5 g/mol + 112 g/mol
Molar mass = 192 g/mol
Finally, we can calculate the number of grams of citric acid:
Grams = 0.003717 moles × 192 g/mol = 0.713 grams
Therefore, there are approximately 0.713 grams of citric acid in the 12.6 mL sample of lime juice.