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Jessica is a scientist - Leaving Cert Mathematics - Question 8 - 2022
Question 8
Jessica is a scientist. Jessica is making up a solution of acid. She has two different bottles, each with the following concentration of the acid: Bottle A: Concen... show full transcript
Worked Solution & Example Answer:Jessica is a scientist - Leaving Cert Mathematics - Question 8 - 2022
Step 1
i) Work out how many ml of acid are in 200 ml of liquid from Bottle A.
Answer
To find the volume of acid in 200 ml of liquid from Bottle A, use the concentration formula:
Volume of acid = Concentration × Volume of liquid
So, ( \text{Volume of acid} = \frac{12}{100} \times 200 = 24 , \text{ml} )
Step 2
ii) Work out the overall concentration of the acid in Jessica’s mixture.
Answer
First, calculate the total volume of acid in the mixture:
- From Bottle A: 24 ml
- From Bottle B: ( 0.05 \times 300 = 15 , \text{ml} )
Total acid = 24 ml + 15 ml = 39 ml.
Total volume of the mixture = 200 ml + 300 ml = 500 ml.
The concentration is calculated as:
[ \text{Concentration} = \frac{\text{Total acid}}{\text{Total volume}} \times 100 ]
[ \text{Concentration} = \frac{39}{500} \times 100 = 7.8% ]
Step 3
iii) Explain why Jessica could not make a solution with a 4% concentration of acid by mixing liquid from Bottle A and Bottle B.
Answer
A 4% concentration requires a specific ratio of liquid from both bottles. However, the minimum concentration from Bottle A is 12%, and from Bottle B is 5%. The lowest possible concentration achievable by combining these liquids is between 5% and 12%, thus making it impossible to get exactly 4%.
Step 4
iv) Work out the percentage error in this measurement.
Answer
The percentage error can be calculated using the formula:
[ \text{Percentage Error} = \frac{|\text{Measured Value} - \text{True Value}|}{\text{True Value}} \times 100 ]
In this case, ( \text{Measured Value} = 260 , \text{ml} ) and ( \text{True Value} = 250 , \text{ml} ):
[ \text{Percentage Error} = \frac{|260 - 250|}{250} \times 100 = \frac{10}{250} \times 100 = 4% ]
Step 5
Step 6
Step 7
iii) Use this equation to find the number of pentagons in the surface of this solid.
Answer
To find p, start with the given equation:
( \frac{6h + 5p}{3} - \frac{6h + 5p}{2} + h + p = 2 ).
Multiply through by 6 to eliminate the fractions:
[ 2(6h + 5p) - 3(6h + 5p) + 6h + 6p = 12 ]
Combine like terms, leading to an equation to solve for p, yielding:
[ p = 12. ]