a solution of h₂so₄(aq) with a molal concentration of 5.25 m has a density of 1.266 g/ml. what is the molar…

Explanation:

Step1: Define molality and molarity concepts

Molality ($m$) is moles of solute per kg of solvent. Molarity ($M$) is moles of solute per liter of solution. Given $m = 5.25\ m$, meaning 5.25 moles of $H_2SO_4$ in 1 kg of water.

Step2: Calculate mass of solute

The molar - mass of $H_2SO_4$ is $M_{H_2SO_4}=(2\times1 + 32+4\times16)\ g/mol=98\ g/mol$. Mass of 5.25 moles of $H_2SO_4$ is $m_{H_2SO_4}=5.25\ mol\times98\ g/mol = 514.5\ g$.

Step3: Calculate mass of solution

Mass of solvent (water) is $m_{solvent}=1000\ g$. Mass of solution $m_{solution}=m_{solute}+m_{solvent}=514.5\ g + 1000\ g=1514.5\ g$.

Step4: Calculate volume of solution

Given density $\rho = 1.266\ g/mL$. Using $\rho=\frac{m}{V}$, we can find volume $V=\frac{m_{solution}}{\rho}=\frac{1514.5\ g}{1.266\ g/mL}\approx1196.3\ mL = 1.1963\ L$.

Step5: Calculate molarity

Molarity $M=\frac{n}{V}$, where $n = 5.25\ mol$ (moles of solute) and $V = 1.1963\ L$. So $M=\frac{5.25\ mol}{1.1963\ L}\approx4.4\ M$.

Answer:

$4.4$