To calculate the molarity and the overall max error and overall % error of the given titres (24.994 mL, 24.948 mL, and 24.934 mL), we will follow these steps:
1. Calculate the mean titre.
First, we find the average (mean) of the three titres:
\[ \text{Mean} = \frac{24.994 , \text{mL} + 24.948 , \text{mL} + 24.934 , \text{mL}}{3} \]
Calculating:
\[ \text{Mean} = \frac{24.994 + 24.948 + 24.934}{3} = \frac{74.876}{3} = 24.95867 , \text{mL} \quad (\text{rounded: } 24.959 , \text{mL}) \]
2. Calculate the absolute error for each titre.
To find the absolute errors of each titre, subtract the mean titre from each individual titre:
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Absolute error for 24.994 mL: \[ \lvert 24.994 - 24.95867 \rvert = 0.03533 , \text{mL} \]
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Absolute error for 24.948 mL: \[ \lvert 24.948 - 24.95867 \rvert = 0.01067 , \text{mL} \]
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Absolute error for 24.934 mL: \[ \lvert 24.934 - 24.95867 \rvert = 0.02467 , \text{mL} \]
3. Calculate the maximum error.
The maximum error is the largest absolute error:
\[ \text{Max Error} = \max(0.03533, 0.01067, 0.02467) = 0.03533 , \text{mL} \]
4. Calculate the overall % error.
First, to calculate the % error for each titre, we use the formula:
\[ \text{Percentage Error} = \left( \frac{\text{Absolute Error}}{\text{Mean}} \right) \times 100 \]
Calculating for the first titre (using the mean):
\[ \text{Percentage Error for } 24.994 = \left( \frac{0.03533}{24.95867} \right) \times 100 \approx 0.141 % \]
Calculating for the second titre:
\[ \text{Percentage Error for } 24.948 = \left( \frac{0.01067}{24.95867} \right) \times 100 \approx 0.043 % \]
Calculating for the third titre:
\[ \text{Percentage Error for } 24.934 = \left( \frac{0.02467}{24.95867} \right) \times 100 \approx 0.099 % \]
To find the overall % error, we can consider the maximum % error:
\[ \text{Max % Error} = 0.141 % \]
Summary
- Mean Titre: 24.959 mL
- Max Error: 0.03533 mL
- Overall % Error: 0.141 %
This calculation provides a good sense of the precision of the titres provided. If you need further calculations about molarity or specific concentration information, please provide additional details regarding moles of solute or the volume of solution involved.
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