Well, if you want to convert 1.5 grams of benzoic acid to its salt, you'll need to react it with sodium hydroxide. The first step is to calculate the number of moles of benzoic acid you have. Since the molar mass of benzoic acid is about 122.12 g/mol, you have:
1.5 g / 122.12 g/mol = 0.0123 mol
Since the balanced equation tells us that one mole of benzoic acid reacts with one mole of sodium hydroxide, you'll need an equal number of moles of sodium hydroxide. So, you'll also need 0.0123 moles of sodium hydroxide.
Now, to find the volume of 3M sodium hydroxide needed, you'll use the number of moles and the molarity of the solution. Molarity is given by the formula:
Molarity = Moles of solute / Volume of solution (in liters)
Rearranging the formula, you can solve for the volume of solution:
Volume of solution (in liters) = Moles of solute / Molarity
So, plugging in the values:
Volume of solution (in liters) = 0.0123 mol / 3M = 0.0041 L
Converting this to milliliters (ml), you get:
Volume of solution (in ml) = 0.0041 L * 1000 ml/L = 4.1 ml
So, you'll need about 4.1 ml of 3M sodium hydroxide to convert 1.5 g of benzoic acid to its salt.
Now, to calculate the volume of 12M HCl needed to convert the sodium benzoate back to benzoic acid. Since the balanced equation tells us that one mole of sodium benzoate reacts with two moles of hydrochloric acid, we'll need twice the number of moles of sodium benzoate to react with the hydrochloric acid.
Since you started with 0.0123 moles of sodium benzoate, you'll need:
2 * 0.0123 mol = 0.0246 mol of hydrochloric acid
Now, using the same formula as before:
Volume of solution (in liters) = Moles of solute / Molarity
You can find the volume of 12M HCl:
Volume of solution (in liters) = 0.0246 mol / 12M = 0.0021 L
Converting this to milliliters:
Volume of solution (in ml) = 0.0021 L * 1000 ml/L = 2.1 ml
So, you'll need about 2.1 ml of 12M HCl to convert the sodium benzoate back to benzoic acid.
Hope that helps! And remember, science is all about balancing equations, just like balancing on a tightrope.