Question

1. a student determines the density of an irregularly shaped block of lead in the laboratory. the displacement volume measured 25.2 ml using a graduated cylinder. the mass on the electric balance reads 285.768 g. what is the density of lead reporting to the appropriate number of significant figures allotted by the equipment used? options: 11.34 g/ml, 11.3 g/ml, 11.340 g/ml, 11 g/ml

Explanation:

Step1: Recall density formula

Density ($
ho$) is calculated by the formula $
ho = \frac{m}{V}$, where $m$ is mass and $V$ is volume.

Step2: Identify values

Mass $m = 285.768$ g, Volume $V = 25.2$ mL.

Step3: Calculate density

Substitute values into the formula: $
ho=\frac{285.768\ \text{g}}{25.2\ \text{mL}}$. Performing the division: $\frac{285.768}{25.2}=11.34$.

Step4: Determine significant figures

The volume (25.2 mL) has 3 significant figures, and the mass (285.768 g) has more. When dividing, the result should have the same number of significant figures as the least precise measurement (3 significant figures here). So we round 11.34 to 3 significant figures, which is 11.3. Wait, no—wait, 25.2 has 3, 285.768 has 6. Wait, no, 25.2 is three significant figures. Wait, 285.768 divided by 25.2: let's check the calculation again. 285.768 ÷ 25.2. Let's do this division: 25.2 × 11 = 277.2, 285.768 - 277.2 = 8.568. 8.568 ÷ 25.2 = 0.34. So total is 11.34. Now, the volume is 25.2 (three significant figures), mass is 285.768 (six). The rule for multiplication/division is that the result has the same number of significant figures as the least number, which is three. Wait, 11.34 rounded to three significant figures: the first three are 1,1,3, the next digit is 4, which is less than 5, so we keep it 11.3? Wait, no, wait 11.34: the third significant figure is 3, the next digit is 4, so rounding 11.34 to three significant figures is 11.3? Wait, no, 11.34: digits are 1 (1st), 1 (2nd), 3 (3rd), 4 (4th). So when rounding to three, look at the fourth: 4 < 5, so 11.3. But wait, wait the volume is 25.2 (three sig figs), mass is 285.768 (six). So the density should be reported to three significant figures. Wait, but let's check the options. The options include 11.3 g/mL. Wait, but wait my calculation was 11.34. Wait, maybe I made a mistake. Wait 285.768 divided by 25.2: let's do this division more accurately. 25.2 × 11.3 = 25.2×11 + 25.2×0.3 = 277.2 + 7.56 = 284.76. 285.768 - 284.76 = 1.008. 1.008 ÷ 25.2 = 0.04. So 11.3 + 0.04 = 11.34. So the exact value is 11.34. Now, the volume is 25.2 (three significant figures), so the density should have three significant figures. 11.34 rounded to three significant figures: the third is 3, next is 4, so 11.3. Wait, but wait 25.2 is three, 285.768 is six. So the limiting factor is three. So the answer should be 11.3 g/mL? Wait, but let's check the options. The first option is 11.34, second is 11.3, third is 11.340, fourth is 11. So according to significant figures, volume is 25.2 (three), mass is 285.768 (six). So the result should have three significant figures. So 11.34 rounded to three is 11.3. So the correct option is 11.3 g/mL. Wait, but wait, maybe I messed up the significant figures. Wait 25.2 has three, 285.768 has six. So when dividing, the number of significant figures is determined by the least, which is three. So 11.34 rounded to three significant figures is 11.3. So the answer is 11.3 g/mL.

Answer:

11.3 g/mL (corresponding to the option "11.3 g/mL")