An Ap student got a lab report back with "-4.5 % error" written in red on it. He had found the boiling point of an unknown liquid to be 45 C. What is the correct boiling point of his unknown liquid?
I know first I would write -4.5 % error = |4.5-x|/x x 100 but I don't know what to do after that.
I would do
[(45-x)/x]*100 = -4.5
45-x/x = -0.045
45-x = -0.045x
45 = x-0.045x
45 = 0.955x
x = 47.12
check:
[(45-47.12)/47.12]*100 =
[-2.12/47.12]*100 = 44.99
I may have used too many significant figures but you get the idea.
You didn’t explain it very good. I didn’t know what to do after what you told me.
To find the correct boiling point, you can set up the equation based on the given -4.5% error as follows:
-4.5% error = |4.5 - x| / x * 100
Let's solve it step-by-step:
1. Convert the percentage to a decimal by dividing it by 100:
-4.5% = -4.5 / 100 = -0.045
2. Rewrite the equation using the absolute value symbol:
-0.045 = |4.5 - x| / x * 100
3. Multiply both sides of the equation by x to eliminate the fraction:
-0.045x = |4.5 - x| * 100
4. Remove the absolute value by considering both the positive and negative cases:
-0.045x = (4.5 - x) * 100 (positive case)
-0.045x = (-4.5 + x) * 100 (negative case)
We will solve each case separately:
Positive Case:
-0.045x = (4.5 - x) * 100
5. Distribute the 100 to the terms inside the parentheses:
-0.045x = 450 - 100x
6. Add 100x to both sides:
0.055x = 450
7. Divide both sides by 0.055:
x = 450 / 0.055 ≈ 8181.82
Therefore, in the positive case, the correct boiling point of the unknown liquid is approximately 8181.82°C.
Negative Case:
-0.045x = (-4.5 + x) * 100
8. Distribute the 100 to the terms inside the parentheses:
-0.045x = -450 + 100x
9. Subtract 100x from both sides:
-100.045x = -450
10. Divide both sides by -100.045:
x = -450 / -100.045 ≈ 4.499
Therefore, in the negative case, the correct boiling point of the unknown liquid is approximately 4.499°C.
In conclusion, the correct boiling point of the unknown liquid could be either approximately 8181.82°C (positive case) or approximately 4.499°C (negative case), depending on the interpretation of the -4.5% error.
To find the correct boiling point of the unknown liquid, we'll use the formula you mentioned:
-4.5% error = |(4.5 - x)| / x * 100
First, let's rewrite the formula as follows:
-4.5 = |4.5 - x| / x * 100
Now let's simplify the equation step by step:
1. Multiply both sides of the equation by x:
-4.5 * x = |4.5 - x| * 100
2. Distribute the multiplication on the left side:
-4.5x = |4.5 - x| * 100
3. Remove the absolute value by considering both possible cases:
3a. If 4.5 - x is positive:
-4.5x = (4.5 - x) * 100
3b. If 4.5 - x is negative:
-4.5x = -(4.5 - x) * 100
4. Solve each case separately:
Case 3a:
-4.5x = (4.5 - x) * 100
Distribute the multiplication on the right side:
-4.5x = 450 - 100x
Combine like terms:
-4.5x + 100x = 450
95.5x = 450
Divide both sides by 95.5:
x = 450 / 95.5
x ≈ 4.71
Case 3b:
-4.5x = -(4.5 - x) * 100
Distribute the multiplication on the right side:
-4.5x = -450 + 100x
Combine like terms:
-4.5x - 100x = -450
-104.5x = -450
Divide both sides by -104.5:
x = -450 / -104.5
x ≈ 4.31
Therefore, the correct boiling point of the unknown liquid could be approximately 4.71 °C or 4.31 °C, depending on the specific context and assumptions made in terms of the positive or negative error.