CHEMISTRY COLLEGE

Iodine-131, t1/2 = 8.0 days, is used in diagnosis and treatment of thyroid gland diseases. If a laboratory sample of iodine-131 initially emits 9.95 × 1018 β particles per day, how long will it take for the activity to drop to 6.22 × 1017 β particles per day?

Answers

Answer 1

Answer:

Explanation:

Formula for the first order decay is as follows.

$ln((A)/(A_(o)))$ = -kt

where, A = activity at time t

$A_(o)$ = initial activity

k = decay constant

Hence, putting the given values into the above formula as follows.

k = $\frac{ln(2)}{\text{half life}}$

= $(ln(2))/(8.0)$

= 0.086643 per day

Also, $(ln(6.22 * 10^(17)))/(9.95 * 10^(8)) = -0.086643 * t$

t = 32 days

Thus, we can conclude that it will take 32 days for the activity to drop to $6.22 * 10^(17)$ $\beta$ particles per day.

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A cubic box with sides of 20.0 cm contains 2.00 × 1023 molecules of helium with a root-mean-square speed (thermal speed) of 200 m/s. The mass of a helium molecule is 3.40 × 10-27 kg. What is the average pressure exerted by the molecules on the walls of the container? (The Boltzmann constant is 1.38 × 10-23 J/K and the ideal gas constant is R = 8.314 J/mol•K .) (12 pts.)

Answers

Answer:

1.133 kPa is the average pressure exerted by the molecules on the walls of the container.

Explanation:

Side of the cubic box = s = 20.0 cm

Volume of the box ,V= $s^3$

$V=(20.0 cm)^3=8000 cm^3=8* 10^(-3) m^3$

Root mean square speed of the of helium molecule : 200m/s

The formula used for root mean square speed is:

$\mu=\sqrt{(3kN_AT)/(M)}$

where,

= root mean square speed

k = Boltzmann’s constant = $1.38* 10^(-23)J/K$

T = temperature = 370 K

M = mass helium = $3.40* 10^(-27)kg/mole$

$N_A$ = Avogadro’s number = $6.022* 10^(23)mol^(-1)$

$T=(\mu _(rms)^2* M)/(3kN_A)$

Moles of helium gas = n

Number of helium molecules = N = $2.00* 10^(23)$

N = $N_A* n$

Ideal gas equation:

PV = nRT

Substitution of values of T and n from above :

$PV=(N)/(N_A)* R* (\mu _(rms)^2* M)/(3kN_A)$

$PV=(N* R* \mu ^2* M)/(3k* (N_A)^2)$

$R=k* N_A$

$PV=(N* \mu ^2* M)/(3)$

$P=(2.00* 10^(23)* (200 m/s)^2* 3.40* 10^(-27) kg/mol)/(3* 8* 10^(-3) m^3)$

$P=1133.33 Pa =1.133 kPa$

(1 Pa = 0.001 kPa)

1.133 kPa is the average pressure exerted by the molecules on the walls of the container.

Final answer:

The question asks for the average pressure exerted by helium gas molecules on the walls of a cubic container. Using the equation PV = Nmv^2, we can calculate pressure by substituting the given values for volume, number of molecules, mass of one molecule, and root-mean-square speed.

Explanation:

The question is asking to calculate the average pressure exerted by helium gas molecules on the walls of a cubic container. The important formula relating pressure (P), volume (V), number of molecules (N), mass of a molecule (m), and the square of the rms speed (v2) of the molecules in a gas is:

PV = Nmv2,

First, we need to determine the volume of the container, which is the cube of one side, so V = (20 cm)3 = (0.2 m)3. Inserting the given values into the equation and solving for P gives us the desired answer. Recall that the rms speed is given, so no temperature calculations are needed.

Therefore, using all given data points:

Volume (V) = (0.2 m)3

Number of molecules (N) = 2.00 × 1023

Mass of one helium molecule (m) = 3.40 × 10-27 kg

Root-mean-square speed (vrms) = 200 m/s

By substituting these values, we can find the pressure exerted by the gas. This represents an application of kinetic theory of gases which assumes the behavior of an ideal gas.

When the reaction mixture is worked-up, it is first washed three times with 5% sodium bicarbonate, and then with a saturated nacl solution. explain why?

Answers

Solution:

After the reaction of mixture is worked-up Washing three times the organic with sodium carbonate helps to decrease the solubility of the organic layer into the aqueous layer. This allows the organic layer to be separated more easily.

And then the reaction washed by saturated NACL we have The bulk of the water can often be removed by shaking or "washing" the organic layer with saturated aqueous sodium chloride (otherwise known as brine). The salt water works to pull the water from the organic layer to the water layer.

Calculate the mass % of magnesium sulfate (assume that there is a 1:1 mol ratio between sulfate and magnesium sulfate) in the original sample. Report your answer without units and use 3 sig figs, i.e. 55.23543% would be entered as 55.2

Answers

61.8 % is the mass percentage of magnesium sulphate.

Explanation:

The mass percent of individual solute or ion in a compound is calculated by the formula:

Grams of solute ÷ grams of solute + solvent × 100

mass percent of magnesium is calculated as 1 mole of magnesium having 24.305 grams/mole will have weight of 24.305 grams and 1 mole of MgSO4 will have 120.366 grams

Putting the values in the equation:

24.305 ÷ 144.671 × 100

= 16.8% of magnesium is in the mixture

The mass percentage of SO4 is calculated as

= 96.06 ÷ 216.426 × 100

= 44.38 %

The mass percentage of the mixture MgSO4 is 44.38 + 16.8 = 61.8 %

Mass percentage is a representation of the concentration of element or elements in a compound.

Calculate the number of C atoms in 9.837 x 1024 molecules of CO2.

Please help

Answers

Answer:

Explanation:

1 molecule contains 1 carbon atom.

9.837 * 10^24 molecules contains 9.837 * 10^24 atom of carbon.

It's a 1 to 1 ratio.

Hydrazine, N2H4, is a weak base and is used as fuel in the space shuttle.N2H4(aq)+H2O(l)âN2H5+(aq)+OHâ(aq)

Part A

If the pH of a 0.133 M solution is 10.66, what is the ionization constant of the base?

Express your answer using two significant figures.

Answers

Answer:

Kb = 1.6*10^-6

Explanation:

The given reaction is:

$N2H4(aq)+H2O(l)\rightarrow N2H5+(aq)+OH-(aq)$

The ionization constant of the base Kb is given as:

$Kb = ([N2H5+][OH-])/([N2H4])------(1)$

The pH = 10.66

therefore, pOH = 14-pH = 14-10.66 =3.34

$[OH-] = 10^(-pOH) =10^(-3.34) =4.57*10^(-4) M$

[N2H5+] = [OH-] = 4.57*10^-4M

[N2H4] = 0.133 M

Based on eq(1)

$Kb = ([4.57*10^(-4)]^(2))/([0.133])=1.6*10^(-6)$

Which expression correctly describes energy using SI units? A. 1 J=1kg•m^2/s^2 B. 1 J= 1kg•m/s^2 C. 1 J= 1kg• m/s D. 1 J= 1kg•m^2/s

Answers

Answer:

A. 1 J=1kg•m^2/s^2

Explanation:

Energy refers to the capacity to do work. According to the International System of units (SI units), energy is measured in Joules.

Energy is represented by the force applied over a distance. Force is measured in Newton (N) and distance in metres (m). Hence, energy is Newton × metre (N.m)

Newton is derived from the SI units of mass (Kilograms), and acceleration (metres per seconds^2) i.e Kg.m/s^2, since Force = mass × acceleration.

Since; Energy = Newton × metres

If Newton = Kg.m/s^2 and metres = m

Energy (J) will therefore be; Kg.m/s^2 × m

1J = Kg.m^2/s^2

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