2.1 Concentration and its measurement

Concentration is crucial in chemical kinetics, affecting reaction rates through collision frequency. It's measured in various ways, including molarity, molality, and mole fraction, each with unique applications and calculations.

Understanding concentration units and their conversions is essential for accurately describing chemical systems. These measurements help predict reaction behavior and are fundamental to kinetics studies across different conditions and mixture compositions.

Concentration and Its Measurement

Concentration in chemical kinetics

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• Concentration refers to the amount of a substance (solute) dissolved in a given volume of a solution
  • Mathematically expressed as the ratio of the amount of solute to the total volume of the solution
• Concentration directly affects the rate of a chemical reaction according to the collision theory
  • Higher concentrations of reactants lead to more frequent collisions between reactant molecules, increasing the reaction rate (NaOH and HCl)
• The rate law describes the relationship between reaction rate and reactant concentrations, often including concentration terms raised to a power (the order of the reaction with respect to that reactant)
  • For a first-order reaction with respect to reactant A, the rate law is expressed as $rate = k[A]$, where $k$ is the rate constant and $[A]$ is the concentration of reactant A (decomposition of N2O5)

Measures of concentration

• Molarity (M) represents the number of moles of solute per liter of solution
  • Calculated as $\frac{moles\,of\,solute}{liters\,of\,solution}$
  • Temperature-dependent due to the change in solution volume with temperature (aqueous NaCl)
• Molality (m) represents the number of moles of solute per kilogram of solvent
  • Calculated as $\frac{moles\,of\,solute}{kilograms\,of\,solvent}$
  • Temperature-independent as the mass of the solvent remains constant with temperature changes (aqueous sugar solutions)
• Mole fraction (x) is the ratio of the number of moles of one component to the total number of moles in the mixture
  • For a two-component system, $x_A = \frac{moles\,of\,A}{moles\,of\,A + moles\,of\,B}$, where $x_A$ is the mole fraction of component A
  • Dimensionless and applicable to both liquid and gas mixtures (ethanol-water mixtures, air)

Calculation of solution concentration

• To calculate the molarity of a solution, divide the number of moles of solute by the volume of the solution in liters
  • Example: 0.5 moles of NaCl dissolved in 2 liters of water results in a molarity of $M = \frac{0.5\,mol\,NaCl}{2\,L\,solution} = 0.25\,M\,NaCl$
• To calculate the molality of a solution, divide the number of moles of solute by the mass of the solvent in kilograms
  • Example: 0.5 moles of NaCl dissolved in 1 kg of water results in a molality of $m = \frac{0.5\,mol\,NaCl}{1\,kg\,H_2O} = 0.5\,m\,NaCl$

Conversion of concentration units

• To convert from molarity to molality, use the equation $molality = \frac{molarity}{density\,of\,solution - (molarity \times molar\,mass\,of\,solute)}$
  • Requires knowledge of the solution density and the solute's molar mass
• To convert from molality to molarity, use the equation $molarity = \frac{molality \times density\,of\,solution}{1 + (molality \times molar\,mass\,of\,solute)}$
  • Requires knowledge of the solution density and the solute's molar mass
• Pay close attention to units and ensure appropriate values are used in calculations when converting between concentration units (mg/L to mol/L, mol/kg to mol/L)