Presentation on theme: "Grade 10 Mixture Problems"— Presentation transcript:
1 Grade 10 Mixture Problems A simple presentation by Mr. Agostini
2 The ProblemA chemistry teacher needs to make 20 L of 40% sulfuric acid solution. The two containers of acid solutions available contain 30% sulfuric acid and 50% sulfuric acid. How many litres of each solution must be mixed to make a container with 40% sulfuric acid solution.
3 The IdeaDid you know: 30% sulfuric acid contain is made up of 30% acid and the rest is water to dilute the solution. So in a 100 L container, 30L is acid and 70 L is water.You are going to mix the containers together to obtain 20 litres of a solution that 40% of it will be sulfuric acid. How many litres from each container will we need to use to make this mixture.If you had to guess, what would you say: Recall 30% acid in one container and 50% in the other. You need 40% in the mixture. How many litres from each mixture do you think we would need.
4 Defining your Variables First Define your variables first: (Remember the last sentence in the question usually tells us what we are looking for)Let x be the amount in L that is poured from container 1 at 30% acid solutionLet y be the amount in L that is poured from container 2 at 50% acid solution
5 Creating your two equations: Equation 1 Equation 1 is usually build on the amount of liquid (in this case) that is required. We need 20 L.Therefore: x amount is being poured in from container 1 and y amount is being poured in from container 2, to make 20 L. Their sum is 20 then.So the equation is:x + y = 20 (Equ: 1)
6 Creating your two equations: Equation 2 We create equation 2 from the amount of pure acid that is needed from each container and how much pure acid is in the 20L container. (Recall: 40% of 20 L of pure acid is required)The amount(L) of pure acid from container 1 will be 30% of x amount(L) poured into the beaker or 0.30x.The amount(L) of pure acid from container 2 will be 50% of y amount(L) poured into the beaker or 0.50yTherefore, we combine 30% of x with 50% of y to obtain 40% of 20 LThe second equation is:0.30x y = 0.40(20) (Equ: 2)
7 So what do we have: Let x = amount in L of 30% sulphuric acid soluton. Let y = amount in L of 50% sulphuric acid soluton.(1) x + y = 20(2) 0.30x y = 0.40(20)Or(2) 0.3x + 0.5y = 8
8 When Solving you can use any method you wish. Yay!!!!! Elimination Method:( x -3)( x 10)-3x – 3y = -603x + 5y = 80Back sub into x + y = 20x + 10 = 20x = 20 – 10x = 10Therefore 10 L of container 1 (at 30% acid solution) and 10 L of container 2 (at 50% acid solution) is needed to make 20 L at 40% acid solution.x + y = 200.3x + 0.5y = 8+2y = 20y = 10
9 When Solving you can use any method you wish. Yay!!!!! Substitution Method:(1) x + y = 20Back sub into x + y = 20(2) 0.3x + 0.5y = 810 + y = 20y = 20 – x sub into (2)y =0.3x + 0.5(20 – x) = 8y = 100.3x + 10 – 0.5x = 8Therefore 10 L of container 1 (at 30% acid solution) and 10 L of container 2 (at 50% acid solution) is needed to make 20 L at 40% acid solution.0.3x – 0.5x =– 0.2x = - 2x = 10