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Half Lives

Nosotros use integrated charge per unit laws, and charge per unit constants to relate concentrations and fourth dimension. The rate constabulary to use depends on the overall order of the reaction.

• Equations for one-half lives
• Determining a half life
• Converting a half life to a rate constant
• Graphical relations and half lives

Equations for Half Lives

For a zero order reaction A products   ,    rate =  thousand:

t_½ =  [A_o] / 2k

For a first social club reaction      A products  ,   rate =  k[A]:

t_½ = 0.693 / one thousand

For a 2d order reaction   2A products   or   A + B products   (when [A] = [B]),      rate = k[A]²:

t_½ = 1 / g [A_o]

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Determining a Half Life

To determine a half life, t_½, the time required for the initial concentration of a reactant to exist reduced to half its initial value, we need to know:

• The guild of the reaction or enough information to determine information technology.
• The charge per unit constant, one thousand, for the reaction or enough information to make up one's mind it.
• In some cases, we need to know the initial concentration, [A_o]

Substitute this information into the equation for the half life of a reaction with this social club and solve for t_½. The equations are given to a higher place.

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Converting a Half Life to a Rate Constant

To catechumen a half life to a rate constant we demand to know:

• The half life of the reaction, t_½.
• The order of the reaction or enough data to make up one's mind it.
• In some cases, we demand to know the initial concentration, [A_o]

Substitute this information into the equation for the half life of a reaction with this order and solve for 1000. The equations are given above.

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Graphical Relations and Half Lives

If we plot the concentration of a reactant versus time, we tin can see the differences in one-half lives for reactions of different orders in the graphs. We can identify a 0, ane^st, or two^nd guild reaction from a plot of [A] versus t past the variation in the time information technology takes the concentration of a reactant to alter by one-half.

• For a zero order reaction (Half life decreases with decreasing concentration.)
• For a 1st order reaction (Half life is constant.)
• For a second order reaction (Half life increases with decreasing concentration.)

For a zero order reaction A products   ,    rate =  k:

For a first order reaction      A products  ,   rate =  thousand[A]:

For a second order reaction   2A products   or   A + B products   (when [A] = [B]),        rate = one thousand[A]^ii:

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Source: https://www.chem.purdue.edu/gchelp/howtosolveit/Kinetics/Halflife.html

Posted by: zamudiofolisn1984.blogspot.com

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