The element with half life of 1.3 billion years have the decay constant of 0.533 billion yrs⁻¹ will take 2.01 billion years to decay to 123 mg from the initial amount of 12 g. Hence, the age of the rock is 2.01 billion years.
What is half life ?Heavy unstable radioactive isotopes undergo nuclear decay by the emission of charged particles. Nuclear decay is a first order reaction.
Thus, the decay constant k = 1/t ln W0/Wt
where t is the time of decay, W0 be the initial amount and Wt be the amount after time t.
The half life of the element = 1.3 billion years
decay constant, k = 0.693/1.3 billion yrs = 0.53 billion yrs⁻¹.
The time taken to decay to 3 mg of its original amount is calculated as follows:
t = 1/k ln Wo/(Wt )
= ln( 12 mg/3 mg)/ 0.53 billion yrs⁻¹.
= 2.01 billion years
Therefore, the time before the element decay to 3 mg from 12 mg is 2.01 billion years. Hence, the age of the rock is 2.01 billion years.
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There are three common functional groups in organic chemistry that are readily ionized by adjusting the ph of the aqueous solution during an extraction. name and write the chemical structure of these three functional groups and show each
moles of hydrogen in 9.15×10−2 mol C4H10
The oceanic crust is made primarily from this type of rock.
Answer:
Igneous rock basalt.
Explanation:
The ocean crust is made mostly of igneous rock basalt, which comes from lava and the movement of tectonic plates.
If 150 g of phenacetin were dissolved in 100 ml of water, how much ether would be required to extract 90% of phenacetin in a single extraction?
what location on earth experiences the least change in the number of daylight hours throughout the year?
Why does ferrocene undergo the acylation reaction more readily than benzene?
One radioactive isotope of calcium has an atomic mass number of 47. How many neutrons are in the calcium-47 nucleus?
Answer: The number of neutrons in the given isotope are 27.
Explanation:
Atomic number is defined as the number of electrons or number of protons that are present in a neutral atom. It is represented as Z.
Z = Atomic number = Number of electrons = Number of protons
Mass number is defined as the sum of number of protons and number of neutrons present in an atom. It is represented as A.
A = Mass number = Number of protons + Number of neutrons
Number of neutrons = Mass number - Atomic number
We are given an isotope having representation: [tex]_{20}^{47}\textrm{Ca}[/tex]
Atomic number or number of protons = 20
Mass number = 47
So, number of neutrons = 47 - 20 = 27
Hence, the number of neutrons in the given isotope are 27.
If a feather and an iron bar is released from a same height in a room without any air resistance, which one(s) will impact the ground first.
A) neither one, because without air resistance gravity is absent
B) iron bar
C) both
D) feather
Both a feather and an iron bar will impact the ground at the same time if released from the same height in a room without air resistance, demonstrating that gravity causes all objects to fall with the same acceleration, disregarding their mass.
Explanation:If a feather and an iron bar are released from the same height in a room without any air resistance, both the feather and the iron bar will impact the ground at the same time. The correct answer is C) both. This outcome occurs because in the absence of air resistance, all objects fall at the same rate due to gravity. This phenomenon was famously demonstrated on the Moon by astronaut David R. Scott in 1971, where, despite the Moon's lower gravitational acceleration of 1.67 m/s² compared to Earth's 9.81 m/s², both a hammer and a feather were shown to fall at the same rate when dropped from the same height. This validates that acceleration due to gravity is constant and does not depend on the mass of the objects involved.
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Find the current through the 30.0 ω resistor.
Without the total voltage or detailed circuit configuration, it's not possible to determine the current through the 30.0 ω resistor. An example using Ohm's law has been provided for a hypothetical scenario.
Explanation:To find the current through the 30.0 ω resistor, we would need to apply Ohm's law, which states that I = V/R, where I is the current, V is the voltage, and R is the resistance. However, the provided information is insufficient to determine the current, as we are not given the total voltage across the resistor or the configuration of the circuit (whether it is series, parallel, or a combination).
If the 30.0 ω resistor were the only resistance in the circuit and the voltage across it was provided, we could directly use Ohm's law to calculate the current. For example, if the voltage was 10 V, the current would simply be I = 10V / 30.0ω = 0.333 A.
Without additional information, such as the configuration of the circuit and the total voltage, we cannot accurately calculate the current. The problem might be missing details or might require knowledge about the rest of the circuit to solve.
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If 50% of radioactive element remains after 4000 years what what is the half life
Which equation best expresses the relationship between pressure and volume for gas?
Suggest a reason for why the phosphorus-containing side product from the horner-emmons wittig reaction is more water-soluble than the triphenylphosphine oxide side product obtained from the standard wittig reaction.
Which of the following represents a compound?
A) H
B) H-3
C)H2O
D) O-16
What needs to happen for a solute to dissolve in a particular solvent?
Answer:
There needs to be a strong interaction between solvent and solute molecules. However, this interaction must be strong enough to disrupt the molecular interactions between the solute molecules.
Explanation:
It is called solute, the chemical compounds that dissolve in another substance. The solvent is the substance into which the solute will be dissolved to form a new product.
Chemical dissolution is the process of dispersing the solute in a solvent, giving rise to a homogeneous solution or mixture. For such a dissolution to occur, an extremely strong chemical bond between the solute and the solvent must occur. However, this bond must be strong enough to separate the bond between the solute molecules.
The essential oil found in cloves, eugenol, can be isolated by steam distillation because it is insoluble in water and has a measurable vapor pressure at 100 °c even though it has a much higher boiling point than water. use data from the table to calculate the volume of eugenol in 30 ml of distillate.
what is the definition of tributary
A tributary is a smaller stream or river that flows into a larger one, contributing to its volume and influencing its navigability, ecosystem, and flooding potential.
Explanation:The definition of a tributary is a stream or river that flows into a larger stream, river, or lake. These smaller watercourses contribute to the flow of the larger one, which is often referred to as the mainstem or parent river. Tributaries do not flow directly into the sea. They provide additional water volume to their parent river, which can then affect the river's ability to navigate, its ecosystem, and potential for flooding. For example, the Missouri River is a tributary of the Mississippi River because it flows into it.
How many grams of CO2 are used when 7.0 g of O2 are produced?
The question cannot be answered as posed because a specific chemical reaction and balanced equation are needed to relate the masses of O2 and CO2.
Explanation:To answer how many grams of CO2 are used when 7.0 g of O2 are produced, we assume the process is a typical combustion or respiration reaction, where CO2 is generated from O2, or vice versa. The balanced chemical equation for the combustion of carbon would typically be C + O2 → CO2. However, since we are given the mass of O2 produced, and not the mass of a carbon-containing fuel that reacts, we cannot proceed to calculate the mass of CO2 without additional information on the specific reaction involved, including the stoichiometry that defines the mass relationship between O2 and CO2. Therefore, we must have a balanced equation or a known reaction to relate the masses of O2 and CO2 produced in order to provide a specific answer.
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9.62 grams of [tex]\( \text{CO}_2 \)[/tex] are used when 7.0 grams of [tex]\( \text{O}_2 \)[/tex] are produced.
One common reaction where [tex]\( \text{O}_2 \)[/tex] is produced and [tex]\( \text{CO}_2 \)[/tex] is consumed is photosynthesis:
[tex]\[ 6 \text{CO}_2 + 6 \text{H}_2\text{O} \rightarrow \text{C}_6\text{H}_{12}\text{O}_6 + 6 \text{O}_2 \][/tex]
From this balanced equation, we see that 6 moles of [tex]\( \text{CO}_2 \)[/tex] produce 6 moles of [tex]\( \text{O}_2 \)[/tex]. This means that 1 mole of [tex]\( \text{CO}_2 \)[/tex] produces 1 mole of[tex]\( \text{O}_2 \).[/tex]
Step-by-Step Solution:
1. Determine the molar mass of [tex]\( \text{O}_2 \)[/tex]:
[tex]\[ \text{Molar mass of O}_2 = 2 \times 16.00 \text{ g/mol} = 32.00 \text{ g/mol} \][/tex]
2. Calculate the moles of \( \text{O}_2 \) produced:
[tex]\[ \text{Moles of O}_2 = \frac{7.0 \text{ g}}{32.00 \text{ g/mol}} = 0.21875 \text{ moles} \][/tex]
3. Use the stoichiometry from the balanced equation:
From the balanced equation, the mole ratio between[tex]\( \text{CO}_2 \) and \( \text{O}_2 \) is 1:1.[/tex]
Therefore, the moles of [tex]\( \text{CO}_2 \)[/tex] used is the same as the moles of [tex]\( \text{O}_2 \)[/tex]produced:
[tex]\[ \text{Moles of CO}_2 = 0.21875 \text{ moles} \][/tex]
4. Determine the molar mass of [tex]\( \text{CO}_2 \)[/tex] :
[tex]\[ \text{Molar mass of CO}_2 = 12.01 \text{ g/mol} + 2 \times 16.00 \text{ g/mol} = 44.01 \text{ g/mol} \][/tex]
5. Calculate the grams of \( \text{CO}_2 \) used:
[tex]\[ \text{Grams of CO}_2 = \text{Moles of CO}_2 \times \text{Molar mass of CO}_2 \][/tex]
[tex]\[ \text{Grams of CO}_2 = 0.21875 \text{ moles} \times 44.01 \text{ g/mol} = 9.62 \text{ g} \][/tex]
How many liters of water are required to dissolve 1.00 g of barium sulfate?
To dissolve 1.00 g of barium sulfate, we would need 1 L of water.
Explanation:In order to calculate the amount of water needed to dissolve 1.00 g of barium sulfate, we need to use the molar mass of barium sulfate and the concept of molarity.
The molar mass of barium sulfate (BaSO4) is 233.43 g/mol. We can use this to convert the mass of barium sulfate to moles.
Once we know the number of moles of barium sulfate, we can use the molar ratio between barium sulfate and water to calculate the volume of water needed. The balanced equation for the dissolution of barium sulfate in water is:
BaSO4 (s) + H2O (l) → Ba2+ (aq) + SO42- (aq)
Based on this equation, 1 mole of barium sulfate dissolves to give 1 mole of water. Therefore, to dissolve 1.00 g of barium sulfate, we would need 1 L of water.
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What is the mass in grams of 6.5×10^20 molecules of aspirin (C9H8O4) ?
The mass in grams of 6.5×10²⁰ molecules of aspirin (C₉H₈O₄) is 0.194 g
From Avogadro's hypothesis,
6.02×10²³ molecules = 1 mole of C₉H₈O₄
Next, we shall determine the mass of 1 mole of C₉H₈O₄.1 mole of C₉H₈O₄ = (12×9) + (1×8) + (16×3)
= 180 g
Therefore, we can say that:
6.02×10²³ molecules = 180 g of C₉H₈O₄
With the above information, we can obtain the mass of 6.5×10²⁰ molecules of aspirin (C₉H₈O₄). This can be obtained as follow:6.02×10²³ molecules = 180 g of C₉H₈O₄
Therefore,
6.5×10²⁰ molecules = [tex]\frac{180 * 6.5*10^{20} }{6.02*10^{23}}\\\\[/tex]
6.5×10²⁰ molecules = 0.194 g
Thus, the mass of 6.5×10²⁰ molecules of aspirin (C₉H₈O₄) is 0.194 g
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The mass in grams of the aspirin is 0.194 g
From the question,
We are to determine the mass in grams of 6.5×10²⁰ molecules of aspirin (C₉H₈O₄)
First, we will determine the number of moles of aspirin present
Using the formula
[tex]Number\ of\ moles = \frac{Number\ of\ molecules}{Avogadro's\ constant}[/tex]
Avogadro's constant = 6.022 × 10²³ mol⁻¹
From the given information
Number of molecules of aspirin = 6.5×10²⁰ molecules
∴ Number of moles of aspirin present = [tex]\frac{6.5 \times 10^{20} }{6.022 \times 10^{23} }[/tex]
Number of moles of aspirin present = 0.0010793756 moles
Number of moles of aspirin present = 1.0793756 ×10⁻³ mole
Now, to determine the mass of aspirin present
From the formula
Mass = Number of moles × Molar mass
Molar mass of aspirin = 180.158 g/mol
∴ Mass of aspirin = 0.0010793756 × 180.158
Mass of aspirin = 0.194458 g
Mass of aspirin = 0.194 g
Hence, the mass in grams of the aspirin is 0.194 g
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What is the mass of 3.00 moles of magnesium chloride, MgCl2? Express your answer with the appropriate units.
The mass of 3.00 moles of magnesium chloride (MgCl₂) is 95.211 gram/mol.
This is determined by multiplying the number of moles by the molar mass of MgCl₂, which is 95.21 g/mol.
To find the mass of 3.00 moles of magnesium chloride (MgCl₂), we need to use the molar mass of MgCl₂ as a conversion factor. The molar mass of MgCl₂ is the sum of the atomic masses of magnesium (Mg) and chlorine (Cl).Steps for Problem Solving:
Determine the atomic masses from the periodic table: Mg = 24.31 g/mol, Cl = 35.45 g/mol.Calculate the molar mass of MgCl₂: Molar mass of MgCl₂ = 24.31 g/mol + 2(35.45 g/mol) = 95.21 g/mol.Use the molar mass to convert moles to grams: Mass (g) = Number of moles × Molar mass (g/mol).Substitute the known values: Mass (MgCl₂) = 3.00 moles × 95.21 g/mol = 285.63 g.Therefore, the mass of 3.00 moles of magnesium chloride (MgCl₂) is 24.305+ 2*35.453= 95.211 gram/mol.
Correct question is: What is the mass of 3.00 moles of magnesium chloride, MgCl₂? Express your answer with the appropriate units.
Is the tetrapeptide ala-glu-gly-lys a good buffer at ph 7.0? will it move in an electric field at ph 7.0?
Give the percent yield when 28.16 g of co2 are formed from the reaction of 8.000 moles of c8h18 with 4.000 moles of o2. 2 c8h18 + 25 o2 → 16 co2 + 18 h2o
equal moles of C8H18 and O2 are reacted to give equal no. of moles of CO2.
mole ratio of C8H18 =(1/2) x 8 = 4 moles
mole ratio of O2 = (1/25) x 4 = 0.16 moles
so, limiting reagent is O2
the no. of moles of CO2 formed = 16 x 0.16 = 2.56 moles
weight of CO2 formed (theoretical weight) = 2.56 x 44 = 112.64
Percentage yield =(practical yiel/theoretical yield) x 100 = (28.16/112.64) x100 = 25%
Answer: The percent yield of carbon-dioxide gas is 25%.
Explanation:
[tex]2C_8H_{18}+25O_2\rightarrow 16CO_2+18H_2O[/tex]
1) According to reaction 25 moles of oxygen gas reacts with 2 moles of [tex]C_8H_{18}[/tex], then 4 moles of oxygen will react with [tex]\frac{2}{25}\times 4[/tex] moles of [tex]C_8H_{18}[/tex] that is 0.32 moles.
Oxygen with 4 moles is limiting reagent in this reaction.
2) According to reaction 25 moles of oxygen gas gives 16 moles of carbon-dioxide gas, then 4 moles of oxygen gas will give [tex]\frac{16}{25}\times 4[/tex] moles of carbon-dioxide gas that is 2.56 moles.
Theoretical mass of [tex]CO_2=\text{number of moles}\times \text{molecular mass of }CO_2}=2.56mol\times 44g/mol=112.64 g[/tex]
Experimental mass of [tex]CO_2[/tex] = 28.16 g
[tex]Percent yield=\frac{|\text{Experimental mass}}{\text{Theoretical mass}}=\frac{28.16\times 100}{112.64}=25\%[/tex]
Hence, the percent yield of carbon-dioxide gas is 25%.
A concentrated solution in water will always contain a strong or weak electrolyte true or false
For each reaction, identify the precipitate or lack thereof bacl2 naoh
If the length of one side of a square is 12.0 m, what is the perimeter of the square? Express the perimeter with the appropriate units
The perimeter of a square whose length is 12.0 m is 48 cm.
Further Explanation Area Area is a measure of how much space is occupied by a given shape.Area of a substance is determined by the type of shape in question.For example;
Area of a rectangle is given by; Length multiplied by widthArea of a triangle = 1/2 x base x heightArea of a circle = πr². where r is the radius of a circle,Area of a square = S², Where s is the side of the square.etc.Perimeter Perimeter is defined as the distance along a two dimension shape. Perimeter of different shapes is given by different formulasFor example;
The perimeter of a rectangle = 2(length+width)The perimeter of a triangle = a+b+c; where a, b and c are the sides of the triangle. etc.In this case;
We are given one side of a square as 12.0 cm
But Perimeter of a square is given by; 4 × s
Thus; Perimeter = 4 × 12 units
= 48 units
Keywords; Perimeter, Area
Learn more about;Perimeter of a square example: brainly.com/question/3619302Area of a square: https://brainly.com/question/1322653Level: Middle school
Subject; Mathematics
Topic: Area and Perimeter
Final answer:
The perimeter of the square with a side length of 12.0 m is 48.0 m.
Explanation:
The perimeter of a square is the sum of all its sides.
Since all the sides of a square are equal, we can find the perimeter by multiplying the length of one side by 4.
For the given square with a side length of 12.0 m, the perimeter would be:
Perimeter = 12.0 m x 4
= 48.0 m
What is the final pressure (expressed in atm) of a 3.05 l system initially at 724 mm hg and 298 k, that is compressed to a final volume of 2.60 l at 273 k?
[tex]\boxed{1.0237596\;{\text{atm}}}[/tex] is the final pressure of a 3.05 L system initially at 724 mm Hg ad 298 K that is compressed to a final volume of 2.60 L at 273 K.
Further Explanation:
An ideal gas is a hypothetical gas that is composed of a large number of randomly moving particles that are supposed to have perfectly elastic collisions among themselves. It is just a theoretical concept and practically no such gas exists. But gases tend to behave almost ideally at a higher temperature and lower pressure.
Ideal gas law is the equation of state for any hypothetical gas. The expression for the ideal gas equation is as follows:
[tex]\boxed{{\mathbf{PV = nRT}}}[/tex] ...... (1)
Here,
P is the pressure of the gas.
V is the volume of the gas.
T is the absolute temperature of the gas.
n is the number of moles of gas.
R is the universal gas constant.
Rearranging equation (1), we get:
[tex]\frac{{PV}}{T} = nR[/tex] ...... (2)
For a particular gas, the number of moles (n) and the universal as constant (R) both are constants.
If a specific gas with [tex]{P_1}[/tex], [tex]{V_1}[/tex] and [tex]{T_1}[/tex] is subjected to any change and the final parameters being [tex]{P_2}[/tex], [tex]{V_2}[/tex] and [tex]{T_2}[/tex]. So equation (2) becomes,
[tex]\frac{{{P_1}{V_1}}}{{{T_1}}} = \frac{{{P_2}{V_2}}}{{{T_2}}}[/tex] ...... (3)
Here,
[tex]{P_1}[/tex] is the initial pressure of the gas.
[tex]{V_1}[/tex] is the initial volume of the gas.
[tex]{T_1}[/tex] is the initial temperature of the gas.
[tex]{P_2}[/tex] is the final pressure of the gas.
[tex]{V_2}[/tex] is the final volume of the gas.
[tex]{T_2}[/tex] is the final temperature of the gas.
Calculation of the final pressure [tex]\left( {{{\mathbf{P}}_{\mathbf{2}}}} \right)[/tex] of the gas
Rearranging equation (3), we get:
[tex]{P_2} = \frac{{{P_1}{V_1}{T_2}}}{{{T_1}{V_2}}}[/tex] ...... (4)
We have [tex]{P_1} = 724\;{\text{mm Hg}}[/tex]
[tex]{V_1} = 3.05\;{\text{L}}[/tex]
[tex]{T_1} = 298\;{\text{K}}[/tex]
[tex]{V_2} = {\text{2}}{\text{.60 L}}[/tex]
[tex]{T_2} = {\text{273 K}}[/tex]
Substitute these values in equation (4).
[tex]\begin{gathered}{P_2}=\frac{{\left( {724\;{\text{mm Hg}}} \right)\left( {3.05\;{\text{L}}} \right)\left( {273\;{\text{K}}} \right)}}{{\left( {298\,{\text{K}}} \right)\left( {2.60\;{\text{L}}} \right)}} \\= 778.05705\;{\text{mm Hg}} \\ \end{gathered}[/tex]
Conversion Factor:
[tex]1\;{\text{mm Hg}} = {\text{0}}{\text{.00131579 atm}}[/tex]
So the value of [tex]{P_2}[/tex] (in atm) is calculated as follows:
[tex]\begin{gathered}{P_2}=\left( {778.05707\;{\text{mm Hg}}}\right)\left( {\frac{{{\text{0}}{\text{.00131579 atm}}}}{{1\;{\text{mm Hg}}}}} \right) \\= 1.023759\;{\text{atm}}\\\end{gathered}[/tex]
So the final pressure of the gas is 1.023759 atm.
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Answer details:
Grade: Senior School
Subject: Chemistry
Chapter: Ideal gas equation
Keywords: ideal gas, pressure, volume, absolute temperature, equation of state, hypothetical, universal gas constant, moles of gas, initial, final, P, V, T, P1, P2, V1, V2, T1, T2.
What is the mass (in grams) of 9.83 × 1024 molecules of methanol (CH3OH)?
How many grams of hydrogen in 4.50 mol H2SO4
What role does the oxidation agent play in a redox reaction
In the shapes and fluid forces lab, you dropped different shapes in the fluid. what was the dependent variable that you observed and recorded
Answer is: Settling time.
Settling is the process by which substances (in this example with different shape) settle to the bottom of the fluid.
The two main variables in an experiment are the independent and dependent variable.
Dependent variable is the variable being tested and measured in a scientific experiment.
Dependent variables depend on the values of independent variables. The dependent variables represent the output or outcome whose variation is being studied.