The quantity concentration of substance is the abbreviation of the quantity concentration of solute substance in solution. Usually, the quantity of solute B(B stands for various solutes) per unit volume is used to represent the physical quantity of solution composition, which is called the quantity concentration of solute B. The quantity concentration of substance is an important concentration expression, which is represented by symbol c(B). The commonly used unit is mole/liter. The basic formula for the quantity and concentration of a substance is:
C (b) = n (b)/v (b stands for various solutes)
Note: ①. V is the volume of the solution, and the unit is generally L. (2). The quantity of substance is the quantity of solute substance, which cannot be expressed by quality.
(3) Take out any volume of the solution, the concentration is constant, and the amount of solute contained is determined by the volume.
(4) The solution is electrically neutral, and the total charges of anions and cations are equal.
When using the formula of quantity and concentration of substances, please pay attention to the following points:
1. Solute, or mass, or volume, hoping to obtain a certain amount of substance. Therefore, we should be familiar with the conversion between the quantity (mol) and the mass (g) and the volume (v).
2. Compared with the mass fraction of solute in solution, the outstanding advantage of the number concentration of substance is that it is easy to know or compare the number of solute particles in solution. The formula of sailing against the current: go in opposite directions: distance sum = speed and * time, time = distance and/speed sum, speed sum = distance and/time.
Go against the sky: distance sum = speed and * time, time = distance and/speed sum, speed sum = distance and/time.
Pursuit problem: distance difference = speed difference * time, time = distance difference/speed difference, speed difference = distance difference/time.
Current problems: speed = ship speed-water speed distance = speed * time, time = distance/speed, speed = distance/time.
Follow the water problem: speed = ship speed+water speed distance = speed * time, time = distance/speed, speed = distance/time.
Sum and difference problem formula
(sum+difference) ÷2= larger number;
(sum and difference) ÷2= smaller number.
Sum-multiple problem formula
And present (multiple+1)= a multiple;
Multiple x multiple = another number,
Or sum-a multiple = another number.
Formula of differential multiple problems
Difference ÷ (multiple-1)= smaller number;
Smaller number x multiple = larger number,
Or decimal+difference = large number.
Average problem formula
Total quantity/total number of copies = average value.
General travel problem formula
Average speed × time = distance;
Distance/time = average speed;
Distance-average speed = time.
The formula of reverse travel problem can be divided into "encounter problem" (two people start from two places and walk in opposite directions) and "separation problem" (two people walk with their backs to each other). Both of these problems can be solved by the following formula:
(speed sum) × meeting (leaving) time = meeting (leaving) distance;
Meet (leave) distance ÷ (speed sum) = meet (leave) time;
Meet (leave) distance-meet (leave) time = speed and.
Formula of the problem of traveling in the same direction
Catch-up (pull-out) distance ÷ (speed difference) = catch-up (pull-out) time;
Catch up (pull away) the distance; Catch-up (pull-away) time = speed difference;
(speed difference) × catching (pulling) time = catching (pulling) distance.
Formula of train crossing bridge problem
(bridge length+conductor) ÷ speed = crossing time;
(Bridge length+conductor) ÷ Crossing time = speed;
Speed × crossing time = the sum of the length of the bridge and the car.
Navigation problem formula
(1) general formula:
Still water speed (ship speed)+current speed (water speed) = downstream speed;
Ship speed-water speed = water flow speed;
(downstream speed+upstream speed) ÷2= ship speed;
(downstream speed-upstream speed) ÷2= water flow speed.
(2) Formula for two ships sailing in opposite directions:
Downstream speed of ship A+downstream speed of ship B = still water speed of ship A+still water speed of ship B.
(3) Formula for two ships sailing in the same direction:
Hydrostatic speed of rear (front) ship-Hydrostatic speed of front (rear) ship = the speed of narrowing (expanding) the distance between two ships.
(Find out the speed of narrowing or widening the distance between the two ships, and then solve it according to the relevant formula above).
For reference only:
Engineering problem formula
(1) general formula:
Efficiency × working hours = total workload;
Total workload ÷ working time = working efficiency;
Total amount of work ÷ efficiency = working hours.
(2) Assuming that the total workload is "1", the formula for solving engineering problems is:
1÷ working time = the fraction of the total amount of work completed in unit time;
1What is the score that can be completed per unit time = working time.
(Note: If the hypothetical method is used to solve the engineering problem, you can arbitrarily assume that the total workload is 2, 3, 4, 5 ... Especially if the total workload is the least common multiple of several working hours, the fractional engineering problem can be transformed into a relatively simple integer engineering problem, and the calculation will become simpler. )
Formula of profit and loss problem
(1) A surplus (surplus) and a deficit (deficit), the formula can be used:
(surplus+deficit) ÷ (the difference between two distributions per person) = number of people.
For example, "children divide peaches, each person 10, 9 less, and 8 more 7s per person." Q: How many children and peaches are there? "
Solution (7+9)÷( 10-8)= 16÷2
=8 (a) ........................................................................................................................................................................
10×8-9=80-9=7 1 (pieces)
Or 8×8+7=64+7=7 1 (pieces) (omitted)
(2) Both times are surplus (surplus), and the formula can be used:
(large surplus-small surplus) ÷ (the difference between two distributions per person) = number of people.
For example, "soldiers carry bullets for marching training, each carrying 45 rounds and more than 680 rounds; If each person brings 50 rounds, then 200 rounds more. Q: How many soldiers are there? How many bullets are there? "
Solution (680-200)÷(50-45)=480÷5
=96 (person)
45×96+680=5000 (hair)
Or 50×96+200=5000 (hair) (omitted)
(3) If twice is not enough (loss), the formula can be used:
(big loss-small loss) ÷ (the difference between two distributions per person) = number of people.
For example, "send a batch of books to students, each with 10 copies, with a difference of 90 copies;" If each person sends 8 copies, there are still 8 copies left. How many students and books are there? "
Solution (90-8)÷( 10-8)=82÷2.
=4 1 (person)
10×4 1-90=320 (this) (omitted)
(4) If one time is not enough (deficit) and the other time is just used up, you can use the formula:
Loss = number of people.
(Example omitted)
(5) One time there is surplus, and the other time it is just used up. This formula can be used to:
Surplus (the difference between two distributions per person) = number of people.
(Example omitted)
Formula of chicken and rabbit problem
(1) Given the total number of heads and feet, find the number of chickens and rabbits:
(total number of feet-number of feet per chicken × total number of heads) ÷ (number of feet per rabbit-number of feet per chicken) = number of rabbits;
Total number of rabbits = number of chickens.
Or (number of feet per rabbit × total head-total feet) ÷ (number of feet per rabbit-number of feet per chicken) = number of chickens;
Total number of chickens = rabbits.
For example, "Thirty-six chickens and rabbits, enough 100. How many chickens and rabbits are there? "
Solution1(100-2× 36) ÷ (4-2) =14 (only)
36- 14=22 (chicken only).
Solution 2 (4×36- 100)÷(4-2)=22 (only) ............................................................................................................................
36-22= 14 (......................... rabbit only).
(short answer)
(2) Given the difference between the total number of chickens and rabbits, when the total number of chickens is greater than that of rabbits, the formula can be used.
(number of feet per chicken × total head-foot difference) ÷ (number of feet per chicken+number of feet per rabbit) = number of rabbits;
Total number of rabbits = number of chickens
Or (the number of feet per rabbit × the total number of heads+the difference between the number of feet of chickens and rabbits) ÷ (the number of feet per chicken+the number of feet exempted from each chicken) = the number of chickens;
Total number of chickens = rabbits. (Example omitted)
(3) Given the difference between the total number of feet of chickens and rabbits, when the total number of feet of rabbits is greater than that of chickens, the formula can be used.
(the number of feet per chicken × the total number of heads+the difference between the number of feet of chickens and rabbits) ÷ (the number of feet per chicken+the number of feet per rabbit) = the number of rabbits;
Total number of rabbits = number of chickens.
Or (the number of feet per rabbit × the total number of heads-the difference between the number of feet of chickens and rabbits) ÷ (the number of feet per chicken+the number of feet per rabbit) = the number of chickens;
Total number of chickens = rabbits. (Example omitted)
(4) The following formula can be used to solve the gain and loss problem (the generalization of the chicken-rabbit problem):
(65438 points +0 number of qualified products × total number of products-total score obtained) ÷ (score of each qualified product+deduction of each unqualified product) = number of unqualified products. Or total number of products-(points deducted for each unqualified product × total number of products+total score obtained) ÷ (points deducted for each qualified product+points deducted for each unqualified product) = number of unqualified products.
For example, "the workers who produce light bulbs in the light bulb factory are paid by points." Each qualified product will get 4 points, while each unqualified product will not be scored, and 15 points will be deducted. A worker produced 1000 light bulbs, and * * * got 3525 points. How many of them are unqualified? "
Solution1(4×1000-3525) ÷ (4+15)
=475÷ 19=25 (pieces)
Solution 21000-(15×1000+3525) ÷ (4+15)
= 1000- 18525÷ 19
= 1000-975=25 (pieces) (omitted)
("the gain and loss problem" is also called "the problem of handling glassware". If the glassware is transported intact, the freight is RMB. })
(5) The problem of chicken-rabbit exchange (the problem of finding the number of chickens and rabbits after knowing the total number of feet and the total number of feet after chicken-rabbit exchange) can be solved by the following formula:
[(sum of total feet twice) ÷ (sum of feet of each chicken and rabbit)+(difference of total feet twice) ÷ (difference of feet of each chicken and rabbit) ÷ 2 = number of chickens;
⊙ (sum of total feet twice) ⊙ (sum of feet of each chicken and rabbit)-(difference of total feet twice) ⊙ (difference of feet of each chicken and rabbit) ⊙2 = number of rabbits.
For example, "There are some chickens and rabbits, and * * * has 44 feet. If the number of chickens and rabbits is reversed, * * * has 52 feet. How many chickens and rabbits are there? "
Solution [(52+44) ÷ (4+2)+(52-44) ÷ (4-2)] ÷ 2
=20÷2= 10 (only applicable)
〔(52+44)÷(4+2)-(52-44)÷(4-2)〕÷2
= 12÷2=6 (only applicable)
Tree planting problem formula
(1) The problem of planting trees on the unclosed line;
Interval number+1= number of trees; (planting trees at both ends)
Road length ÷ section length+1= number of trees.
Or interval number-1= number of trees; (No planting at both ends)
Road length ÷ section length-1= number of trees;
Road length ÷ number of sections = length of each section;
Length of each section × number of sections = road length.
(2) The problem of planting trees on closed lines:
Road length/interval = number of trees;
Road length/number of intervals = road length/number of trees
= length of each interval;
Length of each section × number of sections = length of each section × number of trees = road length.
(3) Planar tree planting:
Total area/area per tree = number of trees
Formulas for Solving Fractions and Percentages
Comparison number ÷ standard number = score (percentage) rate corresponding to comparison number;
Number of growth ÷ standard number = growth rate;
Reduction number ÷ standard number = reduction rate.
perhaps
The difference between two numbers ÷ the smaller number = a few more (one percent) (increase);
The difference between two numbers ÷ the larger number = a few (hundredths) (minus).
Reciprocal formula for increasing or decreasing percentage (percentage)
Growth rate ÷( 1+ growth rate) = reduction rate;
Reduction rate ÷( 1- reduction rate) = growth rate.
How much smaller than the area of Jiaqiu? "
This is an application problem to find the reduction rate according to the growth rate. According to the formula, the answer can be
What percentage? "
This is an application problem of finding the growth rate from the reduction rate. According to the formula, the answer can be as follows
Solution to the application problem of comparison number
Standard number × percentage rate = comparison number corresponding to percentage rate;
Standard number × growth rate = growth number;
Standard number × reduction rate = reduction number;
Standard number × (sum of dichotomy) = sum of two numbers;
Standard number × (difference of dichotomy) = difference of two numbers.
Formula for solving the application problem of standard number
Contrast number ÷ Score (percentage) corresponding to contrast number = standard number;
Growth number ÷ growth rate = standard number;
Reduction number ÷ reduction rate = standard number;
Sum of two numbers and sum of two rates = standard number;
The difference between two numbers ÷ the difference between two rates = standard number;
Formula of square matrix problem
(1) solid square: (number of people on each side of the outer layer) 2= total number of people.
(2) Hollow square:
(number of people on each side of the outermost layer) 2- (number of people on each side of the outermost layer -2× number of layers) 2= number of hollow squares.
perhaps
(number of people on each side of the outermost layer-number of layers) × number of layers× 4 = number of hollow squares.
Total number of people ÷4÷ layers+layers = number of people on each side of the outer layer.
For example, there is a three-story hollow square with 10 people on the outermost layer. How many people are there in the whole square?
Scheme 1 is regarded as a solid square first, so the total number of people is
10× 10= 100 (person)
Then calculate the square of the hollow part. From the outside to the inside, every time you enter a floor, if the number of people on each side is less than 2, you enter the fourth floor, and the number of people on each side is
10-2×3=4 (person)
Therefore, the number of squares in the hollow part is as follows.
4×4= 16 (person)
So the number of people in this hollow phalanx is
100- 16=84 (person)
Solution 2 directly applies the formula. According to the formula of the total number of people in the hollow square matrix
(10-3)×3×4=84 (person)
There are many kinds of interest rate problems. The calculation formulas of common simple interest and compound interest problems are introduced as follows.
(1) simple interest problem:
Principal × interest rate× term = interest;
Principal ×( 1+ interest rate× term) = principal and interest;
Principal and interest and cash (1+ interest rate × term) = principal.
Annual interest rate ÷ 12= monthly interest rate;
Monthly interest rate × 12= annual interest rate.
(2) compound interest:
Principal ×( 1+ interest rate) Number of deposit periods = sum of principal and interest.
For example, "someone deposits 2400 yuan with a term of 3 years, and the monthly interest rate is 10.2 ‰ (that is, monthly interest 1.02). After three years, how much is the principal and interest? "
Solution (1) is calculated at the monthly interest rate.
3 years = 65438+2 months ×3=36 months
2400×( 1+ 10.2%×36)
=2400× 1.3672
= 328 1.28 (yuan)
(2) Use the annual interest rate.
Change the monthly interest rate to the annual interest rate first:
10.2‰× 12= 12.24%
Seek principal and interest again:
2400×( 1+ 12.24%×3)
=2400× 1.3672
= 328 1.28 yuan (omitted)