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Reactant Concentration at given Time t Formula

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Concentration of A at Time t is defined as the amount of substance A present after reacting for a given interval of time t. Check FAQs

A = A 0 \cdot (\frac{k f}{k f + k b}) \cdot ((\frac{k b}{k f}) + \exp (- (k f + k b) \cdot t))

A - Concentration of A at Time t?A₀ - Initial Concentration of Reactant A?k_f - Forward Reaction Rate Constant?k_b - Backward Reaction Rate Constant?t - Time?

Reactant Concentration at given Time t Example

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Here is how the Reactant Concentration at given Time t equation looks like with Values.

Here is how the Reactant Concentration at given Time t equation looks like with Units.

Here is how the Reactant Concentration at given Time t equation looks like.

72.4209 = 100 \cdot (\frac{9.7E-5}{9.7E-5 + 4.2E-5}) \cdot ((\frac{4.2E-5}{9.7E-5}) + \exp (- (9.7E-5 + 4.2E-5) \cdot 3600))

72.4209mol/L = 100mol/L \cdot (\frac{9.7E-5s⁻¹}{9.7E-5s⁻¹ + 4.2E-5s⁻¹}) \cdot ((\frac{4.2E-5s⁻¹}{9.7E-5s⁻¹}) + \exp (- (9.7E-5s⁻¹ + 4.2E-5s⁻¹) \cdot 3600s))

72.4209 = 100 \cdot (\frac{9.7E-5}{9.7E-5 + 4.2E-5}) \cdot ((\frac{4.2E-5}{9.7E-5}) + \exp (- (9.7E-5 + 4.2E-5) \cdot 3600))

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Reactant Concentration at given Time t Solution

Follow our step by step solution on how to calculate Reactant Concentration at given Time t?

FIRST Step Consider the formula

A = A 0 \cdot (\frac{k f}{k f + k b}) \cdot ((\frac{k b}{k f}) + \exp (- (k f + k b) \cdot t))

Next Step Substitute values of Variables

∴

A = 100mol/L \cdot (\frac{9.7E-5s⁻¹}{9.7E-5s⁻¹ + 4.2E-5s⁻¹}) \cdot ((\frac{4.2E-5s⁻¹}{9.7E-5s⁻¹}) + \exp (- (9.7E-5s⁻¹ + 4.2E-5s⁻¹) \cdot 3600s))

Next Step Convert Units

∴

A = 100000mol/m³ \cdot (\frac{9.7E-5s⁻¹}{9.7E-5s⁻¹ + 4.2E-5s⁻¹}) \cdot ((\frac{4.2E-5s⁻¹}{9.7E-5s⁻¹}) + \exp (- (9.7E-5s⁻¹ + 4.2E-5s⁻¹) \cdot 3600s))

Next Step Prepare to Evaluate

∴

A = 100000 \cdot (\frac{9.7E-5}{9.7E-5 + 4.2E-5}) \cdot ((\frac{4.2E-5}{9.7E-5}) + \exp (- (9.7E-5 + 4.2E-5) \cdot 3600))

Next Step Evaluate

∴

A = 72420.9468951839mol/m³

Next Step Convert to Output's Unit

∴

A = 72.4209468951839mol/L

LAST Step Rounding Answer

∴

A = 72.4209mol/L

Reactant Concentration at given Time t Formula Elements

Variables

Functions

Concentration of A at Time t

Concentration of A at Time t is defined as the amount of substance A present after reacting for a given interval of time t.

Symbol: A

Measurement: Molar ConcentrationUnit: mol/L

Note: Value can be positive or negative.

Formulas to find Concentration of A at Time t

Initial Concentration of Reactant A

Initial Concentration of Reactant A is defined as the concentration of the reactant A at time t=0.

Symbol: A₀

Measurement: Molar ConcentrationUnit: mol/L

Note: Value should be greater than 0.

Formulas to find Initial Concentration of Reactant A

Forward Reaction Rate Constant

Forward Reaction Rate Constant is used to define the relationship between the molar concentration of the reactants and the rate of the chemical reaction in forward direction.

Symbol: k_f

Measurement: First Order Reaction Rate ConstantUnit: s⁻¹

Note: Value should be greater than 0.

Formulas to find Forward Reaction Rate Constant

Backward Reaction Rate Constant

Backward Reaction Rate Constant is defined as the relationship between the molar concentration of the reactants and the rate of the chemical reaction in backward direction.

Symbol: k_b

Measurement: First Order Reaction Rate ConstantUnit: s⁻¹

Note: Value should be greater than 0.

Formulas to find Backward Reaction Rate Constant

Time

Time is used to defined as the period of time that is required for the reactant to given a certain amount of product in a chemical reaction.

Symbol: t

Measurement: TimeUnit: s

Note: Value should be greater than -1.

Formulas to find Time

exp

n an exponential function, the value of the function changes by a constant factor for every unit change in the independent variable.

Syntax: exp(Number)

Other formulas in First Order Opposed by First Order Reactions category

Go Product Conc for 1st Order Opposed by 1st Order Rxn given Initial Conc of B greater than 0

x = x eq \cdot (1 - \exp (- k f \cdot (\frac{A 0 + B 0}{B 0 + x eq}) \cdot t))

Go Product Conc of First Order Opposed by First Order Reaction given Initial Conc of Reactant

x = x eq \cdot (1 - \exp (- k f \cdot t \cdot (\frac{A 0}{x eq})))

Go Product Concentration of 1st Order Opposed by 1st Order Reaction at given Time t

x = x eq \cdot (1 - \exp (- (k f + k b) \cdot t))

Go Time taken for 1st Order Opposed by 1st Order Reaction

t = \frac{\ln (\frac{x eq}{x eq - x})}{k f + k b}

How to Evaluate Reactant Concentration at given Time t?

Reactant Concentration at given Time t evaluator uses Concentration of A at Time t = Initial Concentration of Reactant A*(Forward Reaction Rate Constant/(Forward Reaction Rate Constant+Backward Reaction Rate Constant))*((Backward Reaction Rate Constant/Forward Reaction Rate Constant)+exp(-(Forward Reaction Rate Constant+Backward Reaction Rate Constant)*Time)) to evaluate the Concentration of A at Time t, The Reactant Concentration at given Time t formula is defined as the amount of reactant that has not yet reacted after a given interval of time t. Concentration of A at Time t is denoted by A symbol.

How to evaluate Reactant Concentration at given Time t using this online evaluator? To use this online evaluator for Reactant Concentration at given Time t, enter Initial Concentration of Reactant A (A₀), Forward Reaction Rate Constant (k_f), Backward Reaction Rate Constant (k_b) & Time (t) and hit the calculate button.

FAQs on Reactant Concentration at given Time t

What is the formula to find Reactant Concentration at given Time t?

The formula of Reactant Concentration at given Time t is expressed as Concentration of A at Time t = Initial Concentration of Reactant A*(Forward Reaction Rate Constant/(Forward Reaction Rate Constant+Backward Reaction Rate Constant))*((Backward Reaction Rate Constant/Forward Reaction Rate Constant)+exp(-(Forward Reaction Rate Constant+Backward Reaction Rate Constant)*Time)). Here is an example- 0.072421 = 100000*(9.74E-05/(9.74E-05+4.18E-05))*((4.18E-05/9.74E-05)+exp(-(9.74E-05+4.18E-05)*3600)).

How to calculate Reactant Concentration at given Time t?

With Initial Concentration of Reactant A (A₀), Forward Reaction Rate Constant (k_f), Backward Reaction Rate Constant (k_b) & Time (t) we can find Reactant Concentration at given Time t using the formula - Concentration of A at Time t = Initial Concentration of Reactant A*(Forward Reaction Rate Constant/(Forward Reaction Rate Constant+Backward Reaction Rate Constant))*((Backward Reaction Rate Constant/Forward Reaction Rate Constant)+exp(-(Forward Reaction Rate Constant+Backward Reaction Rate Constant)*Time)). This formula also uses Exponential Growth (exp) function(s).

Can the Reactant Concentration at given Time t be negative?

Yes, the Reactant Concentration at given Time t, measured in Molar Concentration can be negative.

Which unit is used to measure Reactant Concentration at given Time t?

Reactant Concentration at given Time t is usually measured using the Mole per Liter[mol/L] for Molar Concentration. Mole per Cubic Meter[mol/L], Mole per Cubic Millimeter[mol/L], Kilomole per Cubic Meter[mol/L] are the few other units in which Reactant Concentration at given Time t can be measured.

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Reactant Concentration at given Time t Formula

Reactant Concentration at given Time t Example

Reactant Concentration at given Time t Solution

Reactant Concentration at given Time t Formula Elements

Other formulas in First Order Opposed by First Order Reactions category

How to Evaluate Reactant Concentration at given Time t?

FAQs on Reactant Concentration at given Time t

Variable Name