homogeneous solution

Examples of homogeneous solution in the following topics:

• Homogeneous versus Heterogeneous Solution Equilibria

  • The equilibrium constants for homogeneous and heterogeneous solutions need to be calculated differently.
  • The former are called homogenous reactions, and the later are called heterogeneous reactions.
  • A homogeneous equilibrium is one in which all of the reactants and products are present in a single solution (by definition, a homogeneous mixture).
  • Reactions between solutes in liquid solutions belong to one type of homogeneous equilibria.
  • The phases may be any combination of solid, liquid, or gas phases, and solutions.

• Molality

  • Molality is a property of a solution that indicates the moles of solute per kilogram of solvent.
  • Molality is an intensive property of solutions, and it is calculated as the moles of a solute divided by the kilograms of the solvent.
  • It is easy to calculate molality if we know the mass of solute and solvent in a solution.
  • This is true for all homogeneous solution concentrations, regardless of if we examine a 1.0 L or 10.0 L sample of the same solution.
  • With this information, we can divide the moles of solute by the kg of solvent to find the molality of the solution:

• Osmotic Pressure

  • A solution is defined as a homogeneous mixture of both a solute and solvent.
  • Solutions generally have different properties than the solvent and solute molecules that compose them.
  • Some special properties of solutions are dependent solely on the amount of dissolved solute molecules, regardless of what that solute is; these properties are known as colligative properties.
  • If a solution consisting of both solute and solvent molecules is placed on one side of a membrane and pure solvent is placed on the other side, there is a net flow of solvent into the solution side of the membrane.
  • Discuss the effects of a solute on the osmotic pressure of a solution

• Introduction to The Four Fundamental Spaces

  • Another fundamental subspace associated with any matrix $A$ is composed by the solutions of the homogeneous equation $A\mathbf{x} = 0$ .
  • Well, take any two such solutions, say $\mathbf{x}$ and $\mathbf{y}$ and we have

• Homogeneous Catalysis

  • Homogeneous catalysis is a class of catalysis in which the catalyst occupies the same phase as the reactants.
  • Catalysts can be classified into two types: homogeneous and heterogeneous.
  • Acid catalysis, organometallic catalysis, and enzymatic catalysis are examples of homogeneous catalysis.
  • Most often, homogeneous catalysis involves the introduction of an aqueous phase catalyst into an aqueous solution of reactants.
  • However, unlike with heterogeneous catalysis, the homogeneous catalyst is often irrecoverable after the reaction has run to completion.

• Alloys

  • An alloy is a mixture or metallic solid solution composed of two or more elements.
  • Complete solid solution alloys give single solid phase microstructure.
  • Partial solutions give two or more phases that may or may not be homogeneous in distribution, depending on thermal history.
  • Complete solid solution alloys give single solid phase microstructure.
  • Partial solutions give two or more phases that may or may not be homogeneous in distribution, depending on thermal history.

• Applications of Second-Order Differential Equations

  • Examples of homogeneous or nonhomogeneous second-order linear differential equation can be found in many different disciplines, such as physics, economics, and engineering.
  • Therefore, we end up with a homogeneous second-order linear differential equation:
  • A solution of damped harmonic oscillator.
  • Identify problems that require solution of nonhomogeneous and homogeneous second-order linear differential equations

• Nonhomogeneous Linear Equations

  • When $f(t)=0$, the equations are called homogeneous second-order linear differential equations.
  • Examples of homogeneous or nonhomogeneous second-order linear differential equation can be found in many different disciplines such as physics, economics, and engineering.
  • In general, the solution of the differential equation can only be obtained numerically.
  • However, there is a very important property of the linear differential equation, which can be useful in finding solutions.
  • Linear differential equations are differential equations that have solutions which can be added together to form other solutions.

• Substances and Mixtures

  • Mixtures take the form of alloys, solutions, suspensions, and colloids.
  • Often separating the components of a homogeneous mixture is more challenging than separating the components of a heterogeneous mixture.
  • Distinguishing between homogeneous and heterogeneous mixtures is a matter of the scale of sampling.
  • In practical terms, if the property of interest is the same regardless of how much of the mixture is taken, the mixture is homogeneous.
  • Mixtures are described as heterogeneous or homogeneous.

• The Chi-Square Distribution: Test for Homogeneity

  • A different test, called the Test for Homogeneity, can be used to make a conclusion about whether two populations have the same distribution.
  • To calculate the test statistic for a test for homogeneity, follow the same procedure as with the Test of Independence.
  • We cannot use the Test for Homogeneity to make any conclusions about how they differ.