Question

a chemistry student needs 80.0 g of acetone for an experiment. by consulting the crc handbook of chemistry and physics, the student discovers that the density of acetone is 0.790 g·cm⁻³. calculate the volume in ml of acetone the student should pour out. round your answer to 3 significant digits.

Explanation:

Step1: Recall density formula

The formula for density is $
ho = \frac{m}{V}$, where $
ho$ is density, $m$ is mass, and $V$ is volume. We need to solve for $V$, so rearrange the formula to $V=\frac{m}{
ho}$.

Step2: Substitute values

Given $m = 80.0\ \text{g}$ and $
ho=0.790\ \text{g·cm}^{-3}$. Note that $1\ \text{cm}^3 = 1\ \text{mL}$, so we can use these units directly. Substitute into the formula: $V=\frac{80.0\ \text{g}}{0.790\ \text{g·cm}^{-3}}$.

Step3: Calculate volume

Perform the division: $\frac{80.0}{0.790}\approx101.2658\ \text{cm}^3$. Since $1\ \text{cm}^3 = 1\ \text{mL}$, the volume in mL is also approximately $101.2658\ \text{mL}$.

Step4: Round to 3 significant digits

The number $101.2658$ rounded to 3 significant digits is $101\ \text{mL}$? Wait, no, wait: 80.0 has 3 significant digits, 0.790 has 3. When dividing, the result should have 3 significant digits. Wait, $\frac{80.0}{0.790}=\frac{80.0}{0.790}\approx101.2658$. Wait, 80.0 is three sig figs, 0.790 is three. So the result should be three sig figs. Wait, 101.2658 rounded to three sig figs: the first three significant digits are 1, 0, 1? Wait no, 101.2658: the first non - zero digit is 1, then 0, then 1, then 2... Wait, no, 101.2658: the number is 101.2658. To three significant digits: look at the fourth digit. The third digit is 1, the fourth is 2, which is less than 5? Wait no, wait 80.0 divided by 0.790: let's recalculate. 80.0 / 0.790: 0.790 * 100 = 79.0, 80.0 - 79.0 = 1.0, so 100 + 1.0/0.790≈100 + 1.2658 = 101.2658. So three significant digits: 101? Wait, no, 101.2658: the first three significant figures are 1, 0, 1? Wait, no, significant figures: leading zeros don't count, but zeros between non - zero digits do. So 101.2658 has five significant figures. To three, we look at the fourth digit. The third digit is 1 (in 101.2658, the digits are 1, 0, 1, 2, 6, 5, 8). Wait, no, 101.2658: the number is 1 (hundreds place), 0 (tens), 1 (ones), 2 (tenths), 6 (hundredths), etc. So the first three significant digits are 1, 0, 1? Wait, no, that can't be. Wait, 80.0 is three sig figs, 0.790 is three. So the result should be three sig figs. Let's do the division more accurately: 80.0 ÷ 0.790. Let's use a calculator: 80 ÷ 0.79 = 101.2658228. So to three significant digits, it's 101? Wait, no, 101.2658228: the third significant digit is 1 (the ones place), the next digit is 2, which is less than 5, so we keep the third digit as is. Wait, but 101.2658: if we take three significant digits, it's 101? Wait, no, wait 101.2658: the number is 1.012658×10². So three significant digits would be 1.01×10², which is 101. Wait, but let's check again. Wait, 80.0 g (three sig figs), density 0.790 g/cm³ (three sig figs). The formula $V = m/
ho$. So $V=80.0/0.790 = 101.2658\ \text{cm}^3=101.2658\ \text{mL}$. Rounded to three significant digits: 101 mL? Wait, no, 101.2658: the first three significant digits are 1, 0, 1? Wait, no, 1 (1st), 0 (2nd), 1 (3rd), 2 (4th). So when rounding to three, we look at the 4th digit, which is 2, so we round down. So 101 mL? Wait, no, wait 101.2658: if we consider three significant figures, it's 101? Wait, but 101 has three significant figures. Wait, but let's check with a calculator: 80 divided by 0.79 is approximately 101.2658, which to three significant digits is 101.

Wait, no, wait 80.0 is three sig figs, 0.790 is three. So the result should have three sig figs. So 101.2658 rounded to three sig figs: the number is 101.2658. The third significant digit is 1 (the digit in the ones place), the next digit is 2, so we don't round up. So 101 mL? Wait, but 101.2658 is closer to 101 than 102? Wait, no, 101.2658: the first three significant digits are 1, 0, 1 (wait, no, 1 is the first, 0 is the second, 1 is the third, 2 is the fourth). So yes, 101.

Wait, but let's do the calculation again: 80.0 / 0.790. Let's compute 80.0 ÷ 0.790:

0.790 × 100 = 79.0

80.0 - 79.0 = 1.0

1.0 ÷ 0.790 ≈ 1.2658

So total volume is 100 + 1.2658 = 101.2658, which is 101 mL when rounded to three significant digits.

Answer:

101 mL