A student wants to analyze the composition of a sample of an unknown metal alloy. They dissolve a 0.500g sample of the alloy in hydrochloric acid to form a solution which is then titrated with sodium hydroxide (NaOH) to neutralize the acid. The volume of the NaOH solution required is 16.50 mL. Assuming the acid reacts with the metal in the alloy according to the formula: M + 2HCl → MCl₂ + H₂, what is the percent composition by mass of Metal M in the alloy?

Question

A student wants to analyze the composition of a sample of an unknown metal alloy. They dissolve a 0.500g sample of the alloy in hydrochloric acid to form a solution which is then titrated with sodium hydroxide (NaOH) to neutralize the acid. The volume of the NaOH solution required is 16.50 mL. Assuming the acid reacts with the metal in the alloy according to the formula: M + 2HCl → MCl₂ + H₂, what is the percent composition by mass

Answer 1

To find the percent composition by mass of Metal M in the alloy, we need to first determine the moles of HCl that reacted with the metal. We can do this by using the titration data with NaOH.1. Calculate the moles of NaOH used in the titration:The volume of NaOH solution required is 16.50 mL. Assuming the concentration of NaOH is given or can be determined, we can calculate the moles of NaOH used in the titration. Let's assume the concentration of NaOH is C_NaOH mol/L.Moles of NaOH = C_NaOH *  16.50 mL *  1 L / 1000 mL  Moles of NaOH = C_NaOH * 0.01650 L2. Determine the moles of HCl that reacted with the metal:Since the balanced equation for the neutralization reaction between NaOH and HCl is:NaOH + HCl  NaCl + HOThe mole ratio between NaOH and HCl is 1:1. Therefore, the moles of HCl that reacted with the metal are equal to the moles of NaOH used in the titration.Moles of HCl = Moles of NaOH = C_NaOH * 0.01650 L3. Calculate the moles of Metal M in the alloy:From the balanced equation of the reaction between the metal and HCl:M + 2HCl  MCl + HThe mole ratio between Metal M and HCl is 1:2. Therefore, the moles of Metal M in the alloy are half the moles of HCl that reacted.Moles of Metal M =  1/2  * Moles of HCl =  1/2  * C_NaOH * 0.01650 L4. Determine the molar mass of Metal M:To find the percent composition by mass of Metal M, we need to know its molar mass. Let's denote the molar mass of Metal M as MM_M.5. Calculate the mass of Metal M in the alloy:Mass of Metal M = Moles of Metal M * MM_MMass of Metal M =  1/2  * C_NaOH * 0.01650 L * MM_M6. Calculate the percent composition by mass of Metal M in the alloy:Percent composition by mass of Metal M =  Mass of Metal M / Total mass of the alloy  * 100Percent composition by mass of Metal M =   1/2  * C_NaOH * 0.01650 L * MM_M / 0.500 g  * 100To find the exact percent composition by mass of Metal M in the alloy, you need to know the concentration of the NaOH solution  C_NaOH  and the molar mass of Metal M  MM_M .