To find the grams of [tex]\( HC_2H_3O_2 \)[/tex] (acetic acid) per liter of the solution from the given molarity, you would follow these steps:
1. Understand the relation between molarity and mass:
Molarity is defined as the number of moles of solute per liter of solution. The formula to convert molarity to grams per liter involves the molar mass of the solute.
2. Identify the given molarity of the solution:
The average molarity of the acetic acid solution is provided as 0.043 M.
3. Find the molar mass of acetic acid [tex]\( HC_2H_3O_2 \)[/tex]:
- Hydrogen (H): 1.008 g/mol, but there are 4 H atoms, so [tex]\( 1.008 \times 4 = 4.032 \)[/tex] g/mol.
- Carbon (C): 12.011 g/mol, but there are 2 C atoms, so [tex]\( 12.011 \times 2 = 24.022 \)[/tex] g/mol.
- Oxygen (O): 15.999 g/mol, but there are 2 O atoms, so [tex]\( 15.999 \times 2 = 31.998 \)[/tex] g/mol.
- Summing these gives the molar mass: [tex]\( 4.032 + 24.022 + 31.998 = 60.052 \)[/tex] g/mol.
4. Calculate the grams of [tex]\( HC_2H_3O_2 \)[/tex] per liter:
To find the mass of acetic acid per liter, multiply the molarity by the molar mass:
[tex]\[
\text{grams per liter} = \text{molarity} \times \text{molar mass}
\][/tex]
Therefore:
[tex]\[
\text{grams per liter} = 0.043 \, \text{M} \times 60.052 \, \text{g/mol} = 2.582236 \, \text{grams}
\][/tex]
So, the solution contains 2.582236 grams of [tex]\( HC_2H_3O_2 \)[/tex] per liter. The numerical answer is: [tex]\(\boxed{2.582236}\)[/tex].
