Answer:
(a) See below
(b) 103.935 °F; 102.235 °F
Explanation:
The equation relating the temperature to time is
[tex]T = T_{0} + \Delta T\left (1 - e^{-t/\tau} \right )[/tex]
1. Calculate the thermometer readings after 0.5 min and 1 min
(a) After 0.5 min
[tex]\begin{array}{rcl}T & = & T_{0} + \Delta T\left (1 - e^{-t/\tau} \right )\\ & = & 100 + 10\left (1 - e^{-0.5/1} \right )\\ & = & 100 + 10\left (1 - e^{-0.5} \right )\\ & = & 100 + 10 (1 - 0.6065)\\ & = & 100 + 10(0.3935)\\ & = & 100 + 3.935\\ & = & 103.935\,^{\circ}F\\\end{array}[/tex]
(b) After 1 min
[tex]\begin{array}{rcl}T & = & T_{0} + \Delta T\left (1 - e^{-t/\tau} \right )\\ & = & 100 + 10\left (1 - e^{-1/1} \right )\\ & = & 100 + 10\left (1 - e^{-1} \right )\\ & = & 100 + 10 (1 - 0.3679)\\ & = & 100 + 10(0.6321)\\ & = & 100 + 6.321\\ & = & 106.321\,^{\circ}F\\\end{array}[/tex]
2. Calculate the thermometer reading after 2.0 min
T₀ =106.321 °F
ΔT = 100 - 106.321 °F = -6.321 °F
t = t - 1, because the cooling starts 1 min late
[tex]\begin{array}{rcl}T & = & T_{0} + \Delta T\left (1 - e^{-(t - 1)/\tau} \right )\\ & = & 106.321 - 6.321\left (1 - e^{-(2 - 1)/1} \right )\\ & = & 106.321 - 6.321\left (1 - e^{-1} \right )\\ & = & 106.321 - 6.321 (1 - 0.3679)\\ & = & 106.321 - 6.321 (0.6321)\\ & = & 106.321 - 3.996\\ & = & 102.325\,^{\circ}F\\\end{array}[/tex]
3. Plot the temperature readings as a function of time.
The graphs are shown below.
To plot the variation of the thermometer reading with time, we need to consider the first-order dynamics of the thermometer. The time constant of the thermometer is 1 min, and it takes approximately 5 time constants to reach steady state. To calculate the thermometer reading at specific times, we can use the formula for first-order dynamics.
Explanation:To plot the variation of the thermometer reading with time, we need to consider the first-order dynamics of the thermometer. The time constant of the thermometer is 1 min, so it takes approximately 5 time constants (or 5 minutes) to reach steady state. After that, when the thermometer is suddenly placed in a bath at 110oF, it will start to change its reading towards the new temperature following the first-order dynamics. Then, at t = 1 min, it is returned to the bath at 100oF and again it starts to change its reading towards the new temperature.
(b) To calculate the thermometer reading at t = 0.5 min, we can use the formula for first-order dynamics: R = R0 + (R1 - R0)(1 - e^(-t/tau)), where R0 is the initial reading, R1 is the final reading, t is the time, and tau is the time constant. Plugging in the values, we get R = 100 + (110 - 100)(1 - e^(-0.5/1)) ≈ 105.3oF. To calculate the thermometer reading at t = 2.0 min, we use the same formula with t = 2.0 and the new R0 would be the reading at t = 1 min, which we can calculate similarly.
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The common laboratory solvent diethyl ether (ether) is often used to purify substances dissolved in it. The vapor pressure of diethyl ether, CH3CH2OCH2CH3, is 463.57 mm Hg at 25°C.
1. In a laboratory experiment, students synthesized a new compound and found that when 21.47 grams of the compound were dissolved in 233.8 grams of diethyl ether, the vapor pressure of the solution was 455.55 mm Hg. The compound was also found to be nonvolatile and a non-electrolyte. What is the molecular weight of this compound?
Answer: 386.0 g/mol
Explanation:
As the relative lowering of vapor pressure is directly proportional to the amount of dissolved solute.
The formula for relative lowering of vapor pressure will be,
[tex]\frac{p^o-p_s}{p^o}=i\times x_2[/tex]
where,
[tex]\frac{p^o-p_s}{p^o}[/tex]= relative lowering in vapor pressure
i = Van'T Hoff factor = 1 (for non electrolytes)
[tex]x_2[/tex] = mole fraction of solute =[tex]\frac{\text {moles of solute}}{\text {total moles}}[/tex]
Given : 21.47 g of compound X is present in 233.8 g of diethyl ether
moles of solute (X) = [tex]\frac{\text{Given mass}}{\text {Molar mass}}=\frac{21.47g}{Mg/mol}[/tex]
moles of solvent (diethyl ether) = [tex]\frac{\text{Given mass}}{\text {Molar mass}}=\frac{233.8g}{74g/mol}=3.160moles[/tex]
[tex]x_2[/tex] = mole fraction of solute =[tex]\frac{\frac{21.47g}{Mg/mol}}{\frac{21.47g}{Mg/mol}+3.160}[/tex]
[tex]\frac{463.57-455.55}{463.57}=1\times \frac{\frac{21.47g}{Mg/mol}}{\frac{21.47g}{Mg/mol}+3.160}[/tex]
[tex]0.017301=1\times \frac{\frac{21.47g}{Mg/mol}}{\frac{21.47g}{Mg/mol}+3.160}[/tex]
[tex]M=386.0g/mol[/tex]
The molecular weight of this compound is 386.0 g/mol
If you started with 0.183 mol of N2 and 0.549 mol of H2, and they completely reacted in the reaction vessel, determine the total moles of gas particles (n) there are during the initial and final conditions. Additionally, determine the ratio of the number of gas particles in the products to that of the reactants, then complete the statements below.
Answer:
Initial we have 0.183 + 3*0.183 = 0.732 moles of gas (those will all be consumed).
In the products we have 0.366 moles of gas
Explanation:
Step 1: Data given
Number of moles of N2 = 0.183 mol
Number of moles of H2 = 0.549 mol
Step 2: The balanced equation:
N2 + 3H2 → 2NH3
Step 3: Calculate the limiting reactant
For 1 mol of N2 we need 3 moles of H2 to produce 2 moles of NH3
There is no limiting reactant. But will be completely consumed
Step 4: Calculate moles of NH3
For 1 mol of N2 we have 2 moles of NH3 produced
For 0.183 moles of N2 we have 2*0.183 = 0.366 moles of NH3 produced
Initial we have 0.183 + 3*0.183 = 0.732 moles of gas (those will all be consumed).
In the products we have 0.366 moles of gas
Answer:
Initially, there are 0.732 mol of gas particles. After the reaction is complete, there are 0.366 mol of gas particles. Therefore, the ratio of product to reactant prticles is 5.0
Explanation:
The wastewater solution from a factory containing high levels of salts needs to be diluted before it can be released into the environment. Therefore, two containers of waste solution are separated by a semipermeable membrane and pressure is applied to one container, forcing only water molecules through the membrane and diluting the waste solution in the other container. As dilution continues, higher and higher pressures are needed to counteract the natural tendency for the water molecules to have a net flow back toward the more concentrated solution. What was the applied pressure at the end of this process if the final concentrations of the solutions were 0.053 M and 0.170 M at a temperature of 23 ∘C?
The applied pressure at the end of this process is P = -2.859atm
Explanation:
Write down the given values
there are concentration of two solutions
S1 = 0.053 M
S2 = 0.170 M
Temperature (T) = 23°C
that is written as 298 K
it can be solved by multiplying ans subtracting the values
P=MR1-MR2
0.053 M * 0.082 * 298 - 0.170 M * 0.082 * 298
= 1.295 - 4.15412
P = -2.859atm
Final answer:
Reverse osmosis is a technique that involves applying pressure to force water molecules from a high concentration solution to a low concentration solution through a semipermeable membrane. This method is commonly used to convert saltwater into freshwater. The concentration of the solutions will determine the amount of pressure required.
Explanation:
When a compartment containing a dilute solution is connected to another compartment containing a concentrated solution by a semipermeable membrane, water molecules move from the dilute solution to concentrated solution. This phenomenon is called osmosis. By applying pressure in the higher concentration solution, water molecules migrate from a high concentration solution to a low concentration solution through a semipermeable membrane. This method is called reverse osmosis water filter system. In this technique, the membrane must be able to tolerate the high pressure, and prevent solute molecules to pass through. This technology certainly works, and it has been used to convert salt (ocean or sea) water into fresh water. With this technique, the water with higher concentration is discharged. Thus, this technology is costly in regions where the water cost is high.
Apply the given electronegativities to each bond in the examples below to see which are polar and which are nonpolar. Multiple bonds are treated the same as single bonds.
H-O-H
O-C-O
H-C-N
Answer:
H-O-H polar
O-C-O nonpolar
H-C-N polar
Explanation:
Looking up the electronegativities of the atoms involved in this question, we have:
Atom Electronegativity
H 2.2
C 2.55
N 3.04
O 3.44
All of the atoms differ in electronegativity resulting in individual dipole moments in H-O, O-C, H-C and C-N bonds. To find if the molecules will be polar we need to consider the structure of the compound to see if there is a resultant dipole moment.
In H-O-H, we have 2 lone pairs of electrons around the central oxygen atom which push the angle H-O-H of the ideal tetrahedral structure to be smaller than 109.5 º resulting in an overall dipole moment making it polar.
In O-C-O, we have two dipole moments that exactly cancel each other in the linear molecule since the central carbon atom does not have lone pairs of electrons since it has 2 double bonds. Therefore the molecule is nonpolar.
In H-C-N, again we have have a central carbon atom without lone pairs of electrons and the shape of the molecule is linear. But, now we have that the dipole moment in C-N is stronger than the H-C dipole because of the difference in electronegativity of nitrogen compared to hydrogen. The molecule has an overall dipole moment and it is polar.
Answer:
H-O-H is polar
O-C-O is non polar
H-C-N is polar
Explanation:
H-O-HThe electronegativity value of H is 2.1 and the Electronegavity value for O is 3.5 which makes the electronegativity difference of 1.4. O has 2 lone pair of electrons which makes the shape non- linear and polar.
O-C-OThe bond between C and O is a double bond. The Electronegativity of O is 3.5 while the Electronegativity value for C is 2.5 which gives the electronegativity difference of 1.0. There are no lone pairs on carbon and the dipole or partial charges on carbon and oxygen cancels out making O-C-O non-polar.
H-C-NThe Electronegativity value of H is 2.1, electronegativity value for C is 2.5 and the electronegativity value for N is 3.0 which makes the molecule to develop partial positive charge on H and partial negative charge on the C-N making the compound polar.
For many purposes we can treat ammonia as an ideal gas at temperatures above its boiling point of . Suppose the pressure on a sample of ammonia gas at is tripled.
Is it possible to change the temperature of the ammonia at the same time such that the volume of the gas doesn't change?
A. yes
B. no
If you answered yes, calculate the new temperature of the gas. Round your answer to the nearest °C.
Answer:
A. yes
594°C
Explanation:
There is some info missing. I think this is the original question.
For many purposes we can treat ammonia (NH₃) as an ideal gas at temperatures above its boiling point of -33 °C. Suppose the pressure on a 6.0 m³ sample of ammonia gas at 16.0°C is tripled. Is it possible to change the temperature of the ammonia at the same time such that the volume of the gas doesn't change? If you answered yes, calculate the new temperature of the gas. Round your answer to the nearest °C.
Given data
V₁ = V₂ = 6.0 m³
T₁ = 16.0°C + 273.15 = 289.2 K
T₂ = ?
P₂ = 3 P₁
Assuming constant volume and ideal gas behavior, we can find the new temperature using the Gay-Lussac's law.
[tex]\frac{P_{1}}{T_{1}} =\frac{P_{2}}{T_{2}} \\T_{2}=\frac{P_{2}.T_{1}}{P_{1}} =\frac{3P_{1}.T_{1}}{P_{1}}=3T_{1}=3 \times 289.2K = 867.6K[/tex]
°C = 867.6K - 273.15 = 594°C
Yes, it is possible to change the temperature of the ammonia gas while keeping the volume constant. The new temperature is approximately -88.6 °C.
Explanation:According to Gay-Lussac's law, for a given amount of gas at constant volume, the pressure and temperature are directly proportional. Therefore, if the pressure is tripled, the temperature of the ammonia gas can be changed in the same proportion to keep the volume constant.
We can use the formula P1/T1 = P2/T2 to calculate the new temperature (T2) when the pressure (P) is tripled. Given that the temperature (T1) is the boiling point of ammonia, we can plug in the values and solve for T2.
Using this formula, we can find that the new temperature is approximately -88.6 °C.
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Determine the identity of the daughter nuclide from the beta decay of 8938Sr.9039Y8536Kr8734Se9038Sr8939Y
Answer: The daughter nuclide formed by the beta decay of given isotope is [tex]_{39}^{89}\textrm{Y}[/tex]
Explanation:
Beta decay is defined as the process in which beta particle is emitted. In this process, a neutron gets converted to a proton and an electron.
The released beta particle is also known as electron.
[tex]_Z^A\textrm{X}\rightarrow _{Z+1}^A\textrm{Y}+_{-1}^0\beta[/tex]
We are given:
Parent isotope = [tex]_{38}^{89}\textrm{Sr}[/tex]
The chemical equation for the beta decay process of [tex]_{38}^{89}\textrm{Sr}[/tex] follows:
[tex]_{38}^{89}\textrm{Sr}\rightarrow _{39}^{89}\textrm{Y}+_{-1}^0\beta[/tex]
Hence, the daughter nuclide formed by the beta decay of given isotope is [tex]_{39}^{89}\textrm{Y}[/tex]
Final answer:
The daughter nuclide from the beta decay of Strontium-89 is Yttrium-89, and the nuclear equation for the decay is 8938Sr → 8939Y + β-.
Explanation:
The question is asking to identify the daughter nuclide from the beta decay of Strontium-89 (8938Sr). In beta decay, a neutron in the nucleus is converted into a proton and a beta particle (an electron) is emitted. The atomic number increases by 1, but the mass number remains the same. Therefore, the daughter nuclide of 8938Sr undergoing beta decay would be 8939Y (Yttrium-89).
The nuclear equation for this decay process would be written as:
8938Sr → 8939Y + β-
Indicate whether each statement is true or false. If you measure the rate constant for a reaction at different temperatures, you can calculate the overall enthalpy change for the reaction. Exothermic reactions are faster than endothermic reactions. If you double the temperature for a reaction, you cut the activation energy in half.
Answer:
False, False, False
Explanation:
Indicate whether each statement is true or false.
If you measure the rate constant for a reaction at different temperatures, you can calculate the overall enthalpy change for the reaction. FALSE. The relation between the rate constant (k) and the activation energy (Ea) is given by the Arrhenius equation, that is, k depends on the Ea, but not on the enthalpy (ΔH).Exothermic reactions are faster than endothermic reactions. FALSE. Whether a reaction is exothermic or endothermic is defined by the sign of the enthalpy. However, as stated previously, the rate constant (and the rate reaction) do not depend on the enthalpy of the reaction.If you double the temperature for a reaction, you cut the activation energy in half. FALSE. The activation energy does not depend on the temperature.When the rate constant should be determined so we cannot calculate the enthalpy change.
The Exothermic reactions should not be faster.
Indication of the statement:here the relationship that lies between the rate constant and the activation energy that should be provided by the Arrhenius equation should be based on the Ea.
In the case when the reaction should be considered as the exothermic so it represent the sign of the enthalpy.
Also, the activation energy does not based upon the temperature.
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The balanced reaction equation for combustion of heptane, C 7 H 16 , is C 7 H 16 + 11 O 2 ⟶ 7 CO 2 + 8 H 2 O If the reaction produced 23.5 g CO 2 , how many grams of heptane were burned? mass: g C 7 H 16 The reaction of limestone with hydrochloric acid is CaCO 3 + 2 HCl ⟶ CaCl 2 + CO 2 + H 2 O If the reaction produced 23.5 g CO 2 , how many grams of HCl reacted? mass: g HCl
Answer:
1) There were 7.65 grams of heptane burned
2) There reacted 38.94 grams of HCl
Explanation:
1) The combustion of heptane
Step 1: Data given
Mass of CO2 = 23.5 grams
Molar mass of CO2 = 44.01 g/mol
Step 2: The balanced equation:
C7H16 + 11O2 ⟶ 7CO2 + 8H2O
Step 3: Calculate moles of CO2
Moles CO2 = mass CO2 / molar mass CO2
Moles CO2 = 23.5 grams / 44.01 g/mol
Moles CO2 = 0.534 moles
Step 4: Calculate moles heptane
For 1 mole of Heptane , we need 11 moles of O2 to produce 7 moles of CO2 and 8 moles of H2O
For 0.534 moles of CO2 we have 0.534/7 = 0.0763 moles of heptane
Step 5: Calculate mass of heptane
Mass of heptane = moles heptane * molar mass heptane
Mass heptane = 0.0763 moles * 100.21 g/mol
Mass heptane = 7.65 grams
2) The reaction of limestone with hydrochloric acid
Step 1: Data given
Mass of CO2 = 23.5 grams
Step 2: The balanced equation:
CaCO3 + 2HCl ⟶ CaCl2 + CO2 + H2O
Step 3: Calculate moles of CO2
Moles CO2 = mass CO2 / molar mass CO2
Moles CO2 = 23.5 grams / 44.01 g/mol
Moles CO2 = 0.534 moles
Step 4: Calculate moles of HCl
For 1 mol of CaCO3 we need 2 moles of HCl to produce 1 mol of CaCl2, 1 mol of CO2 and 1 mol of H2O
For 0.534 moles of CO2 we have 2*0.534 = 1.068 moles of HCl
Step 5: Calculate mass of HCl
Mass HCl = moles HCl * molar mass HCl
Mass HCl = 1.068 moles * 36.46 g/mol
Mass HCl = 38.94 grams
To produce 23.5 g of CO₂, approximately 7.63 g of heptane were burned, and 38.94 g of HCl reacted. By using the molar masses and stoichiometric relationships from the balanced reactions, we can find the required masses. Moles of substances involved were calculated using the molar masses and balanced equations.
Determining Grams of Heptane and HCl Reacted
First, let's find out how many grams of heptane (C₇H₁₆) were burned to produce 23.5 g of CO₂ in the given balanced chemical reaction:
Combustion of Heptane:
Balanced equation: C₇H₁₆ + 11 O₂ ⟶ 7 CO₂ + 8 H₂O
Molar mass of CO₂: 12.01 (C) + 2 × 16.00 (O) = 44.01 g/molMoles of CO₂ produced: 23.5 g ÷ 44.01 g/mol ≈ 0.534 moles CO₂From the balanced equation, 7 moles of CO₂ are produced per 1 mole of heptane. Thus, moles of heptane burned: 0.534 moles CO₂ ÷ 7 ≈ 0.076 moles heptane.Molar mass of heptane (C₇H₁₆): 7 × 12.01 (C) + 16 × 1.01 (H) = 100.23 g/molGrams of heptane burned: 0.076 moles × 100.23 g/mol ≈ 7.63 g.Next, let's determine how many grams of HCl reacted to produce 23.5 g of CO₂ in the reaction between limestone and hydrochloric acid:
Reaction of Limestone with Hydrochloric Acid:
Balanced equation: CaCO₃ + 2 HCl ⟶ CaCl₂ + CO₂ + H₂O
Moles of CO₂ produced: 23.5 g ÷ 44.01 g/mol ≈ 0.534 moles CO₂From the balanced equation, 1 mole of CO₂ is produced per 2 moles of HCl. Thus, moles of HCl reacted: 0.534 moles CO₂ × 2 ≈ 1.068 moles HCl.Molar mass of HCl: 1.01 (H) + 35.45 (Cl) = 36.46 g/molGrams of HCl reacted: 1.068 moles × 36.46 g/mol ≈ 38.94 g.