How many grams of solute should be added in \(100 \mathrm{~g}\) water to get a solution of density \(1.2 \mathrm{~g} / \mathrm{m} 1\) and strength \(5 \%\) (w/v)? (a) \(5 \mathrm{~g}\) (b) \(6 \mathrm{~g}\) (c) \(4.17 \mathrm{~g}\) (d) \(4.35 \mathrm{~g}\)

To calculate the volume, we will use the formula: density = mass / volume Where the density is given as 1.2 g/mL, and we have a total mass of 100g of water + grams of solute. We will call the grams of solute "x". 1.2 g/mL = (100g + x) / volume Since the solute and solvent are being mixed, we can assume that the volume is additive. That means that the volume of the solution equals the sum of the volume of the solute and the volume of the solvent (water). We know that 100g of water has a volume of 100mL because water has a density of 1 g/mL. volume = 100 mL + volume of solute Now, we can substitute this expression for the volume into the density equation. 1.2 g/mL = (100g + x) / (100 mL + volume of solute)

We can use the strength percentage given (5% w/v) to find the quantity of solute in 100mL of the solution. 5% w/v = (grams of solute) / (100 mL) Re-arranging the formula to solve for grams of solute: grams of solute = 0.05 * 100 mL grams of solute = 5g Since the solute has a mass of 5g, we can re-write the expression for the volume of the solute: volume of solute = 5g / density of solute

Now that we have expressions for both the volume and grams of solute, we can substitute them back into the original density equation: 1.2 g/mL = (100g + x) / (100 mL + 5g / density of solute) As the density of the solute cannot be computed in this case, we have to find the value of x with the information given. On analysis we find out that we have to solve for x, taking into account the options given in the question. We will try each of the options given to see which one gives us a density of 1.2 g/mL (a) x = 5g 1.2 g/mL = (100g + 5g) / (100 mL) 1.2 g/mL = 105g / 100 mL 1.2 g/mL = 1.05 g/mL (This does not match the required density) (b) x = 6g 1.2 g/mL = (100g + 6g) / (100 mL) 1.2 g/mL = 106g / 100 mL 1.2 g/mL = 1.06 g/mL (This does not match the required density) (c) x = 4.17g 1.2 g/mL = (100g + 4.17g) / (100 mL) 1.2 g/mL = 104.17g / 100 mL 1.2 g/mL ≈ 1.04 g/mL (This does not match the required density) (d) x = 4.35g 1.2 g/mL = (100g + 4.35g) / (100 mL) 1.2 g/mL = 104.35g / 100 mL 1.2 g/mL ≈ 1.04 g/mL (This does not match the required density) From the above calculations, we can see that none of the options give us the required density of 1.2 g/mL. This indicates that there might be an error in the question, or that the question might contain insufficient information.