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3 years ago

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(6 points) Alice owns 20 grams of a radioactive isotope that has a half-life of ln(4) years. (a) Find an equation for the mass m

(t) of the remaining isotope Alice owns after t years.

1 answer:

Cloud [144]3 years ago

6 0

<u>Answer:</u> The equation to calculate the mass of remaining isotope is $[A]=\frac{20}{10^{-0.217t}}$

<u>Explanation:</u>

The equation used to calculate rate constant from given half life for first order kinetics:

$t_{1/2}=\frac{0.693}{k}$

where,

$t_{1/2}$ = half life of the reaction = $\ln 4=1.386yrs$

Putting values in above equation, we get:

$k=\frac{0.693}{1.386yrs}=0.5yrs^{-1}$

Rate law expression for first order kinetics is given by the equation:

$k=\frac{2.303}{t}\log\frac{[A_o]}{[A]}$

where,

k = rate constant = $0.5yr^{-1}$

t = time taken for decay process

$[A_o]$ = initial amount of the sample = 20 grams

[A] = amount left after decay process = ? grams

Putting values in above equation, we get:

$0.5=\frac{2.303}{t}\log\frac{20}{[A]}$

$[A]=\frac{20}{10^{-0.217t}}$

Hence, the equation to calculate the mass of remaining isotope is $[A]=\frac{20}{10^{-0.217t}}$

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Calculate the initial rate for the formation of C at 25 ∘C, if [A]=0.50M and [B]=0.075M.Express your answer to two significant f

N76 [4]

The question is incomplete, here is the complete question:

Calculate the initial rate for the formation of C at 25°C, if [A]=0.50 M and [B]=0.075 M. Express your answer to two significant figures and include the appropriate units.Consider the reaction

A + 2B ⇔ C

whose rate at 25°C was measured using three different sets of initial concentrations as listed in the following table:

The table is attached below as an image.

<u>Answer:</u> The initial rate for the formation of C at 25°C is $2.25\times 10^{-2}Ms^{-1}$

<u>Explanation:</u>

Rate law is defined as the expression which expresses the rate of the reaction in terms of molar concentration of the reactants with each term raised to the power their stoichiometric coefficient of that reactant in the balanced chemical equation.

For the given chemical equation:

$A+2B\rightleftharpoons C$

Rate law expression for the reaction:

$\text{Rate}=k[A]^a[B]^b$

where,

a = order with respect to A

b = order with respect to B

Expression for rate law for first trial:

$5.4\times 10^{-3}=k(0.30)^a(0.050)^b$ ....(1)

Expression for rate law for second trial:

$1.1\times 10^{-2}=k(0.30)^a(0.100)^b$ ....(2)

Expression for rate law for third trial:

$2.2\times 10^{-2}=k(0.50)^a(0.050)^b$ ....(3)

Dividing 2 by 1, we get:

$\frac{1.1\times 10^{-2}}{5.4\times 10^{-3}}=\frac{(0.30)^a(1.00)^b}{(0.30)^a(0.050)^b}\\\\2=2^b\\b=1$

Dividing 3 by 1, we get:

$\frac{2.2\times 10^{-2}}{5.4\times 10^{-3}}=\frac{(0.50)^a(0.050)^b}{(0.30)^a(0.050)^b}\\\\4.07=2^a\\a=2$

Thus, the rate law becomes:

$\text{Rate}=k[A]^2[B]^1$ ......(4)

Now, calculating the value of 'k' by using any expression.

Putting values in equation 1, we get:

$5.4\times 10^{-3}=k[0.30]^2[0.050]^1\\\\k=1.2M^{-2}s^{-1}$

Calculating the initial rate of formation of C by using equation 4, we get:

$k=1.2M^{-2}s^{-1}$

[A] = 0.50 M

[B] = 0.075 M

Putting values in equation 4, we get:

$\text{Rate}=1.2\times (0.50)^2\times (0.075)^1\\\\\text{Rate}=2.25\times 10^{-2}Ms^{-1}$

Hence, the initial rate for the formation of C at 25°C is $2.25\times 10^{-2}Ms^{-1}$

8 0

3 years ago

What best describes the degree to which a material can transmit Heat A:melting point B:boiling point C: thermal conductivity D:

Oduvanchick [21]

Your answer is going to be C

7 0

3 years ago

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If 5.100 g of c6h6 is burned and the heat produced from the burning is added to 5691 g of water at 21 °c, what is the final temp

emmasim [6.3K]

<span>C6H12 = 6x12 + 6x1 = 78.
The equation indicates that 2x78 = 156g benzene will produce 6542kJ.
Using proportions you can then calculate that
x/6542kJ = 7.9g / 156g
x = 331.3kJ = 331300J.

heat = mass x ΔT x 4.18J/g°
ΔT = 331300J / (5691g x 4.18J/g°) = 13.9°

final temp = 21 + 14° = 35°C</span>

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Which of the following statements does not describe what he structure of an atom an atom has a small dense center called nucleus

nikklg [1K]

Answer:

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3 years ago

If a balloon containing 3000 L of gas at 39°C and 99 kPa rises to an altitude where the pressure is 45.5 kPa and the temperature

ludmilkaskok [199]

$\tt =3000~L\times \dfrac{289}{312}\times \dfrac{99}{45.5}$

<h3>Further explanation</h3>

Given

3000 L of gas at 39°C and 99 kPa to 45.5 kPa and 16°C,

Required

the new volume

Solution

Combined with Boyle's law and Gay Lussac's law

$\tt \dfrac{P_1.V_1}{T_1}=\dfrac{P_2.V_2}{T_2}$

T₁ = 39 + 273 = 312

T₂ = 16 + 273 = 289

Input the value :

V₂ = (P₁V₁.T₂)/(P₂.T₁)

V₂ = (99 x 3000 x 289)/(45.5 x 312)

or we can write it as:

V₂ = 3000 L x (289/312) x (99/45.5)

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3 years ago