Question

1. an 8.65 g sample of an unknown group 2a metal hydroxide is dissolved in 85.0 ml of water. an acid - base indicator is added and the resulting solution is titrated with 2.50 m hcl(aq) solution. the indicator change color signaling that the equivalence point has been reached after 56.9 ml of the hydrochloric acid solution has been added.

a. what is the molar mass of the metal hydroxide?
b. what is the identity of the metal cation: ca²⁺, sr²⁺, ba²⁺?

Explanation:

Step1: Calculate moles of HCl

The formula for moles ($n$) is $n = M\times V$, where $M$ is molarity and $V$ is volume in liters. The volume of HCl $V_{HCl}=56.9\ mL = 0.0569\ L$ and molarity $M_{HCl}=2.50\ M$.
$n_{HCl}=M_{HCl}\times V_{HCl}=2.50\ mol/L\times0.0569\ L = 0.14225\ mol$

Step2: Determine moles of metal hydroxide

The reaction between a group 2A metal hydroxide $M(OH)_2$ and HCl is $M(OH)_2 + 2HCl
ightarrow MCl_2+2H_2O$. The mole - ratio of $M(OH)_2$ to HCl is 1:2. So, $n_{M(OH)_2}=\frac{n_{HCl}}{2}$.
$n_{M(OH)_2}=\frac{0.14225\ mol}{2}=0.071125\ mol$

Step3: Calculate molar mass of metal hydroxide

The molar mass ($MM$) is given by the formula $MM=\frac{m}{n}$, where $m$ is mass and $n$ is number of moles. The mass of the metal hydroxide $m = 8.65\ g$.
$MM_{M(OH)_2}=\frac{8.65\ g}{0.071125\ mol}\approx121.6\ g/mol$

Step4: Calculate molar mass of the metal

Let the molar mass of the metal be $x$. The molar mass of $M(OH)_2$ is $x + 2\times(16 + 1)=x + 34$.
We know $x+34 = 121.6\ g/mol$, so $x=121.6 - 34=87.6\ g/mol$

Step5: Identify the metal cation

The molar mass of $Ca^{2 +}$ is approximately 40.1 g/mol, the molar mass of $Sr^{2+}$ is approximately 87.6 g/mol, and the molar mass of $Ba^{2+}$ is approximately 137.3 g/mol.

Answer:

a. The molar mass of the metal hydroxide is approximately $121.6\ g/mol$.
b. The metal cation is $Sr^{2+}$.