Volume recorded using 100mL Graduated Cylinder (beaker) – 45.8 mL Volume recorded using 100mL Graduated Cylinder (Erlenmeyer Flask) – 46.5 mL Volume recorded using 10mL Graduated Cylinder – 4.98 mL Volume recorded using 500mL Graduated Cylinder – 254 mL Based on the data above: A) How many significant digits can the 100 mL Graduated Cylinder generate? B) What is the uncertainty of the 100 mL graduated Cylinder? + or -? C) How many significant digits can the 10 mL Graduated Cylinder generate based on the data? D) What is the uncertainty of the 10 mL graduated Cylinder? + or -? E) What is the percentage of salt in the salt-water solution? Show all work. The final answer must be in the correct significant digits.
The Correct Answer and Explanation is:
) How many significant digits can the 100 mL Graduated Cylinder generate?
To determine the number of significant digits the 100 mL graduated cylinder can generate, we observe the recorded volumes:
- 45.8 mL and 46.5 mL.
The precision of these measurements is to 1 decimal place (tenths place), indicating that the 100 mL graduated cylinder can reliably measure to 1 decimal place.
Answer: The 100 mL graduated cylinder can generate 3 significant digits.
B) What is the uncertainty of the 100 mL graduated Cylinder? + or -?
The uncertainty is generally determined by the smallest increment that the measuring device can reliably record, which is typically half of the smallest division.
For the 100 mL graduated cylinder, the smallest division is 1 mL, so the uncertainty is half of that, i.e., ±0.5 mL.
Answer: The uncertainty of the 100 mL graduated cylinder is ±0.5 mL.
C) How many significant digits can the 10 mL Graduated Cylinder generate based on the data?
For the 10 mL graduated cylinder, the recorded volume is 4.98 mL. The measurement is reported to two decimal places (hundredths place), indicating that the 10 mL graduated cylinder can reliably measure to 2 decimal places.
Answer: The 10 mL graduated cylinder can generate 3 significant digits.
D) What is the uncertainty of the 10 mL graduated Cylinder? + or -?
As with the 100 mL graduated cylinder, the uncertainty is typically half of the smallest division.
The smallest division on the 10 mL graduated cylinder is 0.1 mL, so the uncertainty is ±0.05 mL.
Answer: The uncertainty of the 10 mL graduated cylinder is ±0.05 mL.
E) What is the percentage of salt in the salt-water solution?
To calculate the percentage of salt in the salt-water solution, we need the mass of salt and the total mass of the solution. The data provided does not directly specify the mass of the salt or the solution, so we would need additional information to complete this calculation. However, assuming you were provided with such data (e.g., mass of salt = 4.98 grams, total mass of the solution = 254 grams):
The percentage of salt in the solution is given by the formula:Percentage of Salt=(Mass of SaltTotal Mass of Solution)×100\text{Percentage of Salt} = \left( \frac{\text{Mass of Salt}}{\text{Total Mass of Solution}} \right) \times 100Percentage of Salt=(Total Mass of SolutionMass of Salt)×100Percentage of Salt=(4.98 g254 g)×100=1.96%\text{Percentage of Salt} = \left( \frac{4.98 \, \text{g}}{254 \, \text{g}} \right) \times 100 = 1.96\%Percentage of Salt=(254g4.98g)×100=1.96%
Since the least number of significant digits in the data is 3 significant digits (from the 10 mL graduated cylinder data), we round the final percentage to 1.96%.
Answer: The percentage of salt in the salt-water solution is 1.96% (rounded to 3 significant digits).
