Question

Zinc Two separate masses of zinc were measured on a laboratory balance. The first zinc sample had a mass of 210.10 g, and the second zinc sample had a mass of 235.10 g. The two samples were combined. The volume of the combined sample was found to be 62.3 \(\mathrm{mL}\) . Express the mass and density of the zinc sample in the correct number of significant figures.

Short answer

The combined mass of the two zinc samples is \(445.20 g\), and the density of the combined sample is \(7.14 \frac{g}{\text{mL}}\).

Step-by-step solution

Combine the mass of the zinc samples

Add the mass of the first sample to the mass of the second sample to find the combined mass of the two samples. \(Mass_{combined} = Mass_{1} + Mass_{2}\) Given: \(Mass_{1} = 210.10 g\) \(Mass_{2} = 235.10 g\)

Calculate the combined mass

Now put the values of given masses into the equation: \(Mass_{combined} = 210.10 g + 235.10 g = 445.20 g\) The combined mass of the two zinc samples is \(445.20 g\). Since the given masses were in 5 significant figures, the combined mass is also written in 5 significant figures.

Calculate the density

In order to find the density, we have the formula: \(Density = \frac{Mass}{Volume}\) Given: \(Volume_{combined} = 62.3 \,\text{mL}\) Now put the values in the equation: \(Density = \frac{445.20 g}{62.3 \,\text{mL}}= 7.144 \frac{g}{\text{mL}}\)

Express the density in the correct number of significant figures

As per the significant figure rules, the result should have the same number of decimal places as the least precise given value, i.e., 3 significant figures in this case. So, rounding the density to 3 significant figures, we get: \(Density = 7.14 \frac{g}{\text{mL}}\) The combined mass of the two zinc samples is \(445.20 g\), and the density of the combined sample is \(7.14 \frac{g}{\text{mL}}\).

Key concepts

Measurement in Chemistry

Understanding the importance of accurate measurement in chemistry is fundamental. Every chemical reaction relies on precise ratios and quantities that define the substances' behavior and the outcome of the reaction. When measuring substances like the mass of zinc in our exercise, chemists use devices such as balances to ensure accuracy. The measurements are reported using significant figures, which communicate the precision of the measurement.

Significant figures are the digits in a measurement that carry meaning contributing to its accuracy. In the zinc example, the mass of both samples is given to five significant figures (210.10 g and 235.10 g), telling us that the balance can measure to the nearest 0.01 g. Ensuring that your calculations reflect the correct number of significant figures is crucial, as it affects the reliability of your results and conclusions in chemistry.

Density Calculation

Density is a physical property that indicates how much mass of a substance is contained in a given volume. It is a key concept when characterizing materials in chemistry. The formula for density is straightforward:
\[Density = \frac{Mass}{Volume}\]
However, calculating the correct value involves not only applying the formula but also using the correct significant figures. For instance, in our zinc example, the density is initially calculated to several decimal places, but it must be reported to match the least precise measurement, which in this case is the volume (62.3 mL) with three significant figures. Therefore, the density of zinc is correctly reported as 7.14 g/mL, a crucial step for accurate scientific reporting and further calculations in experimentations and chemical formulations.

Chemical Mass and Volume

In chemistry, the mass of a substance often relates to the amount of matter present, and volume measures the space that matter occupies. Knowing both is vital in fields such as stoichiometry and material science, where they help to determine the quantities needed for reactions and the properties of materials, respectively.

Just like in the zinc problem, combining masses is a matter of adding them, straightforward arithmetic. However, the subtlety lies in respecting significant figures throughout the process. Furthermore, when volume comes into play, like measuring the zinc's combined volume of 62.3 mL, it's essential to consider the equipment's precision. The volume measurement contributes directly to density calculations which affects how scientists understand the substance's characteristics. Mastering these concepts is essential for success in the field of chemistry and in laboratory practices.