Ask a New Question
Menu

What quantitative relationships were present in your data?

Data
Hot Water
Cold Water
Room Temperature Water
Temperature
107.18
My thermometer kept saying LO, it wouldn't give me a exact number. Sorry.
85.72
Time to Dissolve
1:07.82
5.13.81
1.31.45
Notes/Observations
I could see small parts of the tablet dissolve and break off.
No small bits or anything, all I really saw was vapor. This one however had the cup of water change colors before it fully dissolved.
The dissolving was a bit slower, the water didn't have a trail of small bits of the tablet

7 answers

Based on the data you provided, we can observe a few quantitative relationships and trends related to the dissolution of the tablet in various water temperatures. Here's a breakdown of the data:

Data Summary:

  1. Hot Water:

    • Temperature: 107.18 °F
    • Time to Dissolve: 1:07.82 (minutes:seconds)
    • Observations: Small parts of the tablet dissolve and break off.

  2. Cold Water:

    • Temperature: LO (indicating it was too low to measure accurately)
    • Time to Dissolve: 5:13.81 (minutes:seconds)
    • Observations: The water changed colors but no small bits were visible during dissolution, just vapor.

  3. Room Temperature Water:

    • Temperature: 85.72 °F
    • Time to Dissolve: 1:31.45 (minutes:seconds)
    • Observations: Dissolving was slower, with no visible trail of small bits, but some color change may have occurred.

Quantitative Relationships:

  1. Effect of Temperature on Dissolution Time:

    • Hot water (107.18 °F) has the shortest dissolution time at 1:07.82.
    • Room temperature water (85.72 °F) has a dissolution time of 1:31.45, which is longer than hot water.
    • Cold water (assumed to be below the measuring capacity) had the longest dissolution time at 5:13.81, indicating that lower temperatures significantly hinder the dissolution process.

  2. Order of Dissolution Times:

    • Hot Water < Room Temperature Water < Cold Water
    • This suggests a clear relationship where increasing the temperature of water decreases the time required for the tablet to dissolve.

  3. Observation Correlation:

    • The observations correlate with the dissolution times, where:
      • The hotter the water, the more noticeable the dissolution (small parts breaking off).
      • In cold water, a longer dissolution time resulted in a lack of visible small particles and primarily vapor, suggesting a different physical state in the dissolution process.

Conclusion:

The data indicates a strong quantitative relationship between the temperature of the water and the time it takes for the tablet to dissolve. This suggests that higher temperatures facilitate faster dissolution, while lower temperatures impede it significantly. Additionally, the physical observations match the quantitative findings, highlighting a consistent trend between temperature, time, and observable behavior during dissolution.

What mathematical calculations were needed before you could draw conclusions? Provide an example.

To draw conclusions from the data provided about the dissolution of the tablet in water at different temperatures, several mathematical calculations were necessary. Here are the key calculations involved, along with an example:

1. Time Conversion

  • First, all dissolution times should be converted into a uniform format (e.g., seconds) to facilitate comparisons.

Example Calculation:

  • Hot Water Dissolution Time: 1:07.82

    • Convert to seconds: \( 1 \times 60 + 7.82 = 67.82 \) seconds

  • Room Temperature Water Dissolution Time: 1:31.45

    • Convert to seconds: \( 1 \times 60 + 31.45 = 91.45 \) seconds

  • Cold Water Dissolution Time: 5:13.81

    • Convert to seconds: \( 5 \times 60 + 13.81 = 313.81 \) seconds

2. Comparison of Dissolution Times

  • Once the dissolution times are in a consistent unit (seconds), you can easily compare the times.

Example Calculation:

  • Calculate the difference in dissolution times:
    • Difference between Hot Water and Room Temperature:
      • \( 91.45 - 67.82 = 23.63 \) seconds
    • Difference between Room Temperature and Cold Water:
      • \( 313.81 - 91.45 = 222.36 \) seconds
    • Difference between Hot Water and Cold Water:
      • \( 313.81 - 67.82 = 245.99 \) seconds

3. Analysis of Relationships

  • Use the dissolution times to establish ratios or percentages to quantify how much longer it takes to dissolve in one temperature of water compared to another.

Example Calculation:

  • Percentage increase in dissolution time from Hot Water to Cold Water:
    • \( \frac{(313.81 - 67.82)}{67.82} \times 100 = \frac{245.99}{67.82} \times 100 \approx 362.08% \)

This calculation shows that it takes approximately 362.08% longer for the tablet to dissolve in cold water compared to hot water.

Conclusion

Before reaching conclusions about the dissolution behavior of the tablet in different water temperatures, calculations were necessary for:

  • Converting time formats to a consistent unit,
  • Comparing the dissolution times using differences,
  • Analyzing relationships through percentages or ratios.

These mathematical calculations provided the necessary foundation to understand the quantitative relationships present in the experimental data and to validate the observational trends.

find the dissolution time from Hot Water to Cold Water percentage

To calculate the percentage increase in dissolution time from hot water to cold water, we can use the following formula:

\[ \text{Percentage Increase} = \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \times 100 \]

Step 1: Identify the Values

  • Dissolution Time in Hot Water: \( 67.82 \) seconds
  • Dissolution Time in Cold Water: \( 313.81 \) seconds

Step 2: Plug the Values into the Formula

\[ \text{Percentage Increase} = \frac{313.81 - 67.82}{67.82} \times 100 \]

Step 3: Calculate the Difference

\[ \text{Difference} = 313.81 - 67.82 = 245.99 \text{ seconds} \]

Step 4: Calculate the Percentage Increase

\[ \text{Percentage Increase} = \frac{245.99}{67.82} \times 100 \approx 362.08% \]

Conclusion:

The dissolution time in cold water is approximately 362.08% longer than in hot water. This means that it takes significantly longer for the tablet to dissolve in cold water compared to hot water.

shorter and easier to type pls

Sure! Here’s a more concise version:

Percentage Increase in Dissolution Time from Hot Water to Cold Water

  1. Hot Water Time: 67.82 seconds
  2. Cold Water Time: 313.81 seconds

Calculation:

\[ \text{Percentage Increase} = \left( \frac{313.81 - 67.82}{67.82} \right) \times 100 = \left( \frac{245.99}{67.82} \right) \times 100 \approx 362.08% \]

Conclusion: The dissolution time in cold water is about 362.08% longer than in hot water.