Question

Write the equation relating osmotic pressure to the concentration of a solution. Define all the terms, and specify their units.

Short answer

The equation is \( \Pi = iCRT \) with terms defined as osmotic pressure (atm), the van't Hoff factor (unitless), concentration (mol/L), gas constant (L atm K⁻¹ mol⁻¹), and temperature (K).

Step-by-step solution

Identify the Osmotic Pressure Equation

The equation that relates osmotic pressure to the concentration of a solution is the van't Hoff equation. This can be expressed as \( \Pi = iCRT \).

Define Osmotic Pressure \( \Pi \)

Osmotic pressure \( \Pi \) is the pressure required to stop the osmotic flow of water. It is typically measured in atmospheres (atm), but it can also be expressed in other pressure units like Pascals (Pa) or millimeters of mercury (mmHg).

Define the Van't Hoff Factor \( i \)

The van't Hoff factor \( i \) represents the number of particles the solute dissociates into in solution. It is a unitless quantity.

Define the Molar Concentration \( C \)

Molar concentration \( C \) is the number of moles of solute per liter of solution. Its unit is moles per liter \( \text{mol/L} \) or molarity (M).

Define the Universal Gas Constant \( R \)

The universal gas constant \( R \) is a constant that appears in many fundamental equations in the physical sciences, including the ideal gas law. Its value is approximately \( 0.0821 \text{ L atm K}^{-1} \text{ mol}^{-1} \).

Define the Temperature \( T \)

Temperature \( T \) in the equation is measured in Kelvins (K). It represents the absolute temperature at which the measurements are taken.

Key concepts

van't Hoff equation

The van't Hoff equation is an essential formula in chemistry that relates osmotic pressure to the concentration of a solution. It is commonly expressed as \( \Pi = iCRT \), where:

• \( \Pi \) is the osmotic pressure
• \( i \) is the van't Hoff factor
• \( C \) is the molar concentration of the solution
• \( R \) is the universal gas constant
• \( T \) is the temperature in Kelvins

This equation helps to predict how a solution will behave when dealing with osmotic pressure. Understanding each component and how they interact is crucial for solving osmotic pressure problems effectively. Osmotic pressure is a key concept in fields like biology and chemistry, as it plays a major role in processes such as the movement of water across cell membranes.

molar concentration

Molar concentration, often referred to as molarity, is a measure of the concentration of a solute in a solution. It is defined as the number of moles of solute per liter of solution. The unit of molar concentration is usually noted as moles per liter \( \text{mol/L} \) or simply M.

• Molarity indicates how many "units" of a substance are present in a given volume of liquid.
• This concept is crucial for preparing chemical solutions with precise concentrations for various experiments.

Imagine you want to prepare a sugar solution; knowing the molarity helps you determine how much sugar is needed for a desired concentration. This calculation is vital in making solutions with exact chemical properties.

universal gas constant

The universal gas constant, symbolized as \( R \), is a key factor in several pivotal equations in the physical sciences, such as the ideal gas law and the van't Hoff equation. Its value is approximately \( 0.0821 \text{ L atm K}^{-1} \text{ mol}^{-1} \).

• It provides a bridge between macroscopic and microscopic quantities, linking molecular behavior with measurable quantities of gases.
• This constant is instrumental in calculations involving gases and their interactions under varying conditions of temperature and pressure.

In the context of the van't Hoff equation, \( R \) helps relate osmotic pressure to temperature and concentration, underpinning the consistent behavior of gases across different conditions. Each term in the units of \( R \) refers to a physical quantity impacted by the gas constant, supporting its role in diverse chemical calculations.

temperature in Kelvins

Temperature is a measure of the average kinetic energy of particles in a substance. In scientific calculations, especially those involving thermodynamics and the van't Hoff equation, temperature is measured in Kelvins (K). This absolute scale starts from absolute zero, the theoretical point where all molecular motion ceases.

• Using Kelvins provides a direct correlation to energy and avoids negative temperature values.
• This makes it essential for calculations in the van't Hoff equation, where temperature in K ensures consistency in the mathematical relationship.

Converting Celsius to Kelvin is straightforward: add 273.15 to the Celsius temperature. This conversion is crucial when performing calculations to ensure accurate results, especially when dealing with energy changes and reactions at various temperatures.