A dilute aqueous solution of an organic compound soluble in water is formed by dissolving 2.35 g of the compound in water to form 0.250 L of solution. The resulting solution has an osmotic pressure of 0.605 atm at 25 °C. Assuming that the organic compound is a nonelectrolyte, what is its molar mass?

검증된 단계별 안내

Step 1: Understand the problem. We are given the mass of the solute, the volume of the solution, and the osmotic pressure. We are asked to find the molar mass of the solute. The formula for osmotic pressure is: \(\Pi = n/V * R * T\), where \(\Pi\) is the osmotic pressure, n is the number of moles of solute, V is the volume of the solution, R is the ideal gas constant, and T is the temperature in Kelvin.

Step 2: Convert the temperature from Celsius to Kelvin. The formula to convert Celsius to Kelvin is: \(K = °C + 273.15\).

Step 3: Rearrange the osmotic pressure formula to solve for n, the number of moles of solute: \(n = \Pi * V / (R * T)\).

Step 4: Calculate the number of moles of solute using the values given in the problem for osmotic pressure, volume, the ideal gas constant (0.0821 L*atm/K*mol), and the temperature in Kelvin.

Step 5: Calculate the molar mass of the solute. The formula for molar mass is: \(Molar Mass = mass of solute (g) / number of moles\).

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Osmotic Pressure

Osmotic pressure is the pressure required to prevent the flow of solvent into a solution through a semipermeable membrane. It is directly proportional to the concentration of solute particles in the solution and can be calculated using the formula π = iCRT, where π is the osmotic pressure, i is the van 't Hoff factor (which is 1 for nonelectrolytes), C is the molarity of the solution, R is the ideal gas constant, and T is the temperature in Kelvin.

Molarity

Molarity is a measure of concentration defined as the number of moles of solute per liter of solution. It is expressed in moles per liter (mol/L). To find the molarity of a solution, you can use the formula M = n/V, where n is the number of moles of solute and V is the volume of the solution in liters. This concept is essential for calculating the molar mass of the solute from the osmotic pressure.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It can be calculated by dividing the mass of the solute by the number of moles present in the solution. In this context, once the molarity is determined from the osmotic pressure, the molar mass can be derived by rearranging the formula to find the number of moles and using the mass of the solute provided.