Question

Osmotic Cell Disruption Use the van’t Hoff relationship to estimate the osmotic pressure drop across the membrane of a cell undergoing rupture in a 0.01 M salt solution, assuming the internal salt concentration is 0.2 M and that all salts are fully dissociated. Would you call this a negligible, ordinary, or large pressure drop? Why?

Short answer

The osmotic pressure can be calculated using the given values in Van’t Hoff relationship. The magnitude of the obtained pressure will decide whether it's a negligible, ordinary, or large pressure drop. Without calculated numeric values, a definitive categorization cannot be specified.

Step-by-step solution

Understanding the Van't Hoff relationship

The Van't Hoff equation for calculating the osmotic pressure (\( \Pi \)) is given by the formula, \( \Pi = iCRT \), where \(i\) is the Van't Hoff factor, \(C\) is the molar concentration, \(R\) is the gas constant, and \(T\) is the temperature in Kelvin.

Determining the Van't Hoff factor

As we're dealing with salts that are fully dissociated in this problem, the Van't Hoff factor (\(i\)) equals 2. This is because salts fully dissociate into two ions upon solvation.

Calculating the osmotic pressure

Plug the known values into the equation: \(\Pi = iCRT\) where \(i\) equals 2, \(C\) is equal to the difference between the internal and external salt concentration, hence 0.2 - 0.01 = 0.19 M, \(R\) is the ideal gas constant (0.0821 L atm/(mol K)), and \(T\) is the temperature in Kelvin. Assume room temperature (25 Celsius) if not given and convert it to Kelvin: 25 + 273.15 = 298.15 K. The osmotic pressure can be now calculated.

Evaluating the pressure drop

After finding the value of the osmotic pressure, it's necessary to categorize this as a negligible, ordinary, or large pressure drop. This can often be subjective and may depend upon the context of the field of study. But, as a rule of thumb, anything below 1 atm can usually be considered negligible, 1-10 atm as ordinary, and above 10 atm as significant.

Key concepts

Van't Hoff Equation

The Van't Hoff Equation is an important formula for calculating osmotic pressure across a membrane. This is particularly useful in understanding the physical dynamics within biological cells. The formula is given by: \[ \Pi = iCRT \]where:- \( \Pi \) represents osmotic pressure,- \( i \) is the Van't Hoff factor,- \( C \) stands for the molar concentration difference, - \( R \) is the ideal gas constant,- \( T \) is the temperature measured in Kelvin.
This equation helps us predict how pressure changes when the solution concentrations inside and outside a cell differ. By knowing the osmotic pressure, scientists can assess how substances move through cell membranes.

Cell Membrane Rupture

Cell membrane rupture can occur when the osmotic pressure difference across the cell membrane is too high. This pressure difference can cause water to either enter or leave the cell rapidly, leading to potential cell burst or dehydration. When cells are subjected to environments with different salt concentrations, the osmotic pressure can force water to move in or out to balance the concentration: - If the external concentration is low (hypotonic), water may enter the cell leading to swelling. - If the external concentration is high (hypertonic), water leaves the cell causing shrinkage or rupture. This pressure dynamic is critical in assessing whether the pressure drop is negligible, ordinary, or large. Understanding this helps avoid damage to cells due to abrupt changes in external environments.

Salt Dissociation

Salt dissociation refers to the process by which a salt compound breaks into its constituent ions when dissolved in water. In the context of osmotic pressure calculation, this involves figuring out the number of ions formed from a salt. For a salt like NaCl,- As it dissolves, it separates into Na\(^{+}\) and Cl\(^{-}\), meaning the dissociation factor, \( i \), is equal to 2.
This is central to osmotic pressure calculations since the number of ions affects the Van't Hoff factor, which directly influences the pressure value. Understanding salt dissociation is key to accurately predicting how a solution's properties change.

Ideal Gas Constant

The Ideal Gas Constant, denoted by \( R \), is a fundamental constant used in various chemical calculations. Its value is approximately 0.0821 L atm/(mol K). This constant provides a bridge that connects pressure, volume, and temperature in calculations. In the Van't Hoff equation: - \( R \) helps calculate osmotic pressure by linking the concentration of a solution and temperature.The inclusion of \( R \) in the Van't Hoff Equation ensures that the relationship between these variables is accurately represented, allowing for precise calculations of pressure dynamics across cell membranes.