You're absolutely correct in your calculation for part (a)! Let’s walk through the full solution and then answer part (b) clearly.
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Part (a): Calculate the density of the element
Given:
- Sample mass = 12.74 g
- Volume of water = 25.0 mL
- Volume of water + sample = 32.3 mL
Step 1: Find the volume of the sample
We use the
water displacement method:
> Volume of sample = (Volume of water + sample) – (Volume of water)
> Volume of sample = 32.3 mL – 25.0 mL =
7.3 mL
✔ *Note: The subtraction gives 7.3 mL, which has 2 significant figures because 32.3 and 25.0 both have one decimal place, so the difference is reported to one decimal place — but in terms of sig figs for subtraction, we look at decimal places, not total digits. However, since 32.3 – 25.0 = 7.3, and both numbers are precise to the tenths place, the result is also precise to the tenths place → 7.3 has 2 significant figures.*
Step 2: Use the density formula
> Density (D) = mass / volume
> D = 12.74 g / 7.3 mL
> D ≈ 1.745... g/mL
Step 3: Apply significant figures
- Mass = 12.74 g → 4 sig figs
- Volume = 7.3 mL → 2 sig figs (limiting factor)
👉 When multiplying or dividing, the answer must have the same number of significant figures as the measurement with the
least number of sig figs.
So,
round to 2 significant figures:
>
Density = 1.7 g/mL
✔ Your work is correct!
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Part (b): What error is introduced if the volume of the sample is determined before the mass?
This is a
very important lab technique question.
If you measure the
volume first (by submerging the sample in water), the sample will come out
wet — it will be covered in water droplets.
Then, when you place it on the balance to measure its mass,
you’re measuring the mass of the sample PLUS the mass of the water clinging to it.
➡️ This causes the
measured mass to be higher than the true mass of the dry sample.
Since density = mass / volume,
- If mass is too high → density will be
too high.
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✔ Final Answers:
a) Density =
1.7 g/mL
*(Work shown: D = 12.74 g / 7.3 mL = 1.7 g/mL, rounded to 2 significant figures)*
b) Measuring volume before mass introduces
error due to water adhering to the sample, which increases the measured mass and thus results in an
overestimated (too high) density value.
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Great job on your initial calculation — you nailed part (a)! Just make sure to explain part (b) fully like above for full credit. 😊
Parent Tip: Review the logic above to help your child master the concept of density questions worksheet.
