Questions: The osmotic pressure exerted by a solution is equal to the molarity multiplied by the absolute temperature and the gas constant R. Suppose the osmotic pressure of a certain solution is measured to be 12 atm at an absolute temperature of 309 K. Write an equation that will let you calculate the molarity c of this solution. Your equation should contain only symbols. Be sure you define each symbol other than R. Your equation: Definitions of your symbols: =12 atm =309 K

The osmotic pressure exerted by a solution is equal to the molarity multiplied by the absolute temperature and the gas constant R. Suppose the osmotic pressure of a certain solution is measured to be 12 atm at an absolute temperature of 309 K. Write an equation that will let you calculate the molarity c of this solution. Your equation should contain only symbols. Be sure you define each symbol other than R. Your equation: Definitions of your symbols: =12 atm =309 K
Transcript text: The osmotic pressure exerted by a solution is equal to the molarity multiplied by the absolute temperature and the gas constant $R$. Suppose the osmotic pressure of a certain solution is measured to be 12. atm at an absolute temperature of $309 . \mathrm{K}$. Write an equation that will let you calculate the molarity $c$ of this solution. Your equation should contain only symbols. Be sure you define each symbol other than $R$. Your equation: Definitions of your symbols: $\square=12 . \mathrm{atm}$ $\square=309 . \mathrm{K}$
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Solution

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Solution Steps

Step 1: Understanding the Osmotic Pressure Equation

The osmotic pressure (\(\Pi\)) of a solution is given by the equation: \[ \Pi = cRT \] where:

  • \(\Pi\) is the osmotic pressure,
  • \(c\) is the molarity of the solution,
  • \(R\) is the gas constant,
  • \(T\) is the absolute temperature in Kelvin.
Step 2: Rearranging the Equation to Solve for Molarity

To find the molarity \(c\), we rearrange the equation: \[ c = \frac{\Pi}{RT} \]

Step 3: Defining the Symbols

We need to define the symbols used in the equation:

  • \(\Pi = 12 \, \text{atm}\) (osmotic pressure),
  • \(T = 309 \, \text{K}\) (absolute temperature).

Final Answer

\[ \boxed{c = \frac{\Pi}{RT}} \] Definitions of symbols:

  • \(\Pi = 12 \, \text{atm}\)
  • \(T = 309 \, \text{K}\)
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