A nitric acid solution flows at a constant rate of 5L/min into a large tank that initially held 200L of a 0.5% nitric acid solution. The solution inside the tank is kept well stirred and flows out of the tank at a rate of 10L/min. If the solution entering the tank is 10% nitric acid, determine the volume of nitric acid in the tank after t minutes.
Answers
Answer:
x(t) = −39e
−0.03t + 40.
Explanation:
Let V (t) be the volume of solution (water and
nitric acid) measured in liters after t minutes. Let x(t) be the volume of nitric acid
measured in liters after t minutes, and let c(t) be the concentration (by volume) of
nitric acid in solution after t minutes.
The volume of solution V (t) doesn’t change over time since the inflow and outflow
of solution is equal. Thus V = 200 L. The concentration of nitric acid c(t) is
c(t) = x(t)
V (t)
=
x(t)
200
.
We model this problem as
dx
dt = I(t) − O(t),
where I(t) is the input rate of nitric acid and O(t) is the output rate of nitric acid,
both measured in liters of nitric acid per minute. The input rate is
I(t) = 6 Lsol.
1 min
·
20 Lnit.
100 Lsol.
=
120 Lnit.
100 min
= 1.2 Lnit./min.
The output rate is
O(t) = (6 Lsol./min)c(t) = 6 Lsol.
1 min
·
x(t) Lnit.
200 Lsol.
=
3x(t) Lnit.
100 min
= 0.03 x(t) Lnit./min.
The equation is then
dx
dt = 1.2 − 0.03x,
or
dx
dt + 0.03x = 1.2, (1)
which is a linear equation. The initial condition condition is found in the following
way:
c(0) = 0.5% = 5 Lnit.
1000 Lsol.
=
x(0) Lnit.
200 Lsol.
.
Thus x(0) = 1.
In Eq. (1) we let P(t) = 0.03 and Q(t) = 1.2. The integrating factor for Eq. (1) is
µ(t) = exp Z
P(t) dt
= exp
0.03 Z
dt
= e
0.03t
.
The solution is
x(t) = 1
µ(t)
Z
µ(t)Q(t) dt + C
= Ce−0.03t + 1.2e
−0.03t
Z
e
0.03t
dt
= Ce−0.03t +
1.2
0.03
e
−0.03t
e
0.03t
= Ce−0.03t +
1.2
0.03
= Ce−0.03t + 40.
The constant is found using x(t) = 1:
x(0) = Ce−0.03(0) + 40 = C + 40 = 1.
Thus C = −39, and the solution is
x(t) = −39e
−0.03t + 40.
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Answers
Answer:
An X-ray photon of wave length 0.989 nm strikes a surface. The emitted electron has a kinetic energy of 969 eV. What is the binding energy of the electron in kJ/mol? [KE=
1
2
mv2;1 electron volt (eV)=1.602×10−19J][KE=
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1
mv
2
;1 electron volt (eV)=1.602
Final answer:
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Explanation:
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Learn more about Photoelectric Effect here:
#SPJ12
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Alkali metals
Noble Gases
Lanthanides
Answers
Answer:
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Explanation:
they have less valence electrons and therefore are more reactive
Answers
Answer:
precipitate
Explanation:
Precipitation is the creation of a solid from a solution. When the reaction occurs in a liquid solution, the solid formed is called the 'precipitate'. The chemical that causes the solid to form is called the 'precipitant'.
hope i helped :)
Answers
anonymous 5 years ago
First you chlorinate it in presence of light.
C2H6 + Cl2 ---hv -> C2H5Cl + HCl
Then you add aqeuos KOH to get C2H5OH
C2H5Cl+KOH-> C2H5OH+ KCl.
Then you add KMnO4 to get the rquired compound.
C2H5OH ----KMnO4 ---> CH3COOH.
Answers
Answer:
The specific heat of magnesium is 1.04 J/g°C.
Explanation:
Heat lost by the magnesium = Q
Mass of the magnesium = m = 62.08 g
Heat capacity of magnesium= c = ?
Initial temperature of the magnesium =
Final temperature of the magnesium= T = 35.60 °C
Heat absorbed by coffee cup calorimeter = Q'
Heat capacity of coffee cup calorimeter = C = 1.79 J/°C
Initial temperature of coffee cup calorimete = = 23.19°C
Final temperature of coffee cup calorimete = T = 35.60 °C
Heat absorbed by the water = q
Mass of water = m' = 77.81 g
Heat capacity of water = c' = 4.18 J/g°C
Initial temperature of water = = 0°C
Final temperature of water = T
According law of conservation of energy , energy lost by coffee will equal to heat required to raise temperature of water and coffee cup calorimeter.
On solving we get:
c = 1.04 J/g°C
The specific heat of magnesium is 1.04 J/g°C.
music for three hours each day. Plant D does not listen to any music at all.
1. Based on the experiment in the scenario, which visual aid would be most helpful in showing the change in the plants' heights over time?
O A. A line graph
O B. A pie chart
OC. A bar graph
O D. A timeline
Answers
Answer:
A. A line graph
Explanation:
You use line graphs to track changes over time. Line graphs are better when the changes are small. They are also more useful when you want to compare changes over the same period for more than one group, for example, plants exposed to music and a control group.
B is wrong. A pie chart is best for comparing parts of a whole.
C is wrong. You can use a bar graph to track changes over time, but small changes are harder to spot.
D is wrong. You use a timeline to mark important points in time, for example, when you are deciding the times when you must complete various stages of a project.
Which of the charts below do you think is more helpful in showing the change in plant height over time?