Transcribed image text: The ionic compound NaBr is soluble in water. Calculate the osmotic pressure (in atm) generated when 7.70 grams of sodium bromide are dissolved in 94.1 mL of an aqueous solution at 298 K. The van’t Hoff factor for NaBr in this solution is 1.94. atm
The Correct Answer and Explanation is:
To calculate the osmotic pressure (π) of a solution, we use the van’t Hoff equation: π=iMRT\pi = iMRT
Where:
- π\pi = osmotic pressure (in atm)
- ii = van’t Hoff factor (number of particles the solute breaks into)
- MM = molarity of the solution (mol/L)
- RR = ideal gas constant = 0.08206 L·atm/mol·K
- TT = temperature in Kelvin (K)
Step 1: Calculate moles of NaBr
Molar mass of NaBr = 22.99 (Na) + 79.90 (Br) = 102.89 g/mol Moles of NaBr=7.70 g102.89 g/mol=0.07487 mol\text{Moles of NaBr} = \frac{7.70 \text{ g}}{102.89 \text{ g/mol}} = 0.07487 \text{ mol}
Step 2: Convert volume to liters
94.1 mL=0.0941 L94.1 \text{ mL} = 0.0941 \text{ L}
Step 3: Calculate molarity
M=0.07487 mol0.0941 L=0.7956 mol/LM = \frac{0.07487 \text{ mol}}{0.0941 \text{ L}} = 0.7956 \text{ mol/L}
Step 4: Plug values into van’t Hoff equation
π=(1.94)(0.7956 mol/L)(0.08206 L\cdotpatm/mol\cdotpK)(298 K)\pi = (1.94)(0.7956 \text{ mol/L})(0.08206 \text{ L·atm/mol·K})(298 \text{ K}) π=1.94×0.7956×0.08206×298=37.71 atm\pi = 1.94 \times 0.7956 \times 0.08206 \times 298 = 37.71 \text{ atm}
✅ Final Answer:
Osmotic pressure = 37.7 atm
Explanation (≈300 words)
Osmotic pressure is the pressure required to stop the flow of solvent through a semipermeable membrane from pure solvent into a solution. This property depends on the concentration of solute particles, not their identity—making it a colligative property.
Sodium bromide (NaBr) is an ionic compound that dissociates in water into two ions: Na⁺ and Br⁻. Ideally, one formula unit of NaBr yields two particles, so the ideal van’t Hoff factor would be 2. However, due to ion pairing in real solutions, the actual van’t Hoff factor is often slightly less. In this problem, it’s given as 1.94, indicating partial ion association.
We first calculated the number of moles of NaBr using its molar mass and the given mass (7.70 g). Next, we converted the volume of the solution from milliliters to liters to determine molarity (mol/L). Molarity tells us how many moles of solute are present in each liter of solution.
Then we applied the van’t Hoff equation: π=iMRT\pi = iMRT
Here, the constants R=0.08206 L\cdotpatm/mol\cdotpKR = 0.08206 \text{ L·atm/mol·K} and temperature T=298 KT = 298 \text{ K} were used. Multiplying all values together gave the final osmotic pressure of 37.7 atm, a relatively high pressure due to the strong dissociation of NaBr and the concentrated nature of the solution.
This calculation is crucial in biological and chemical systems where osmotic pressure affects processes like nutrient absorption, water balance in cells, and drug delivery.
