Question

You calculate that you need \(10.0123576 \mathrm{~g}\) of \(\mathrm{NaCl}\) for an experiment. What amount should you measure out if the precision of the balance is (a) \(+\) or \(-0.01 \mathrm{~g}\) ? (b) \(+\) or \(-0.001 \mathrm{~g}\) ? (c) + or \(-0.0001 \mathrm{~g}\) ?

Short answer

For (a): 10.01 g, for (b): 10.012 g, for (c): 10.0124 g.

Step-by-step solution

Understand the Required Amount

The exact amount of \(\text{NaCl}\) needed for the experiment is given as 10.0123576 grams. This is the target amount that should be measured with the available balance.

Precision of the Balance for Case (a)

The precision of the balance in case (a) is \( \pm 0.01 \text{g} \). This means the balance can measure within a range of 0.01 grams. Based on this precision: \[\text{Measured Amount for (a)} = 10.0123576 \text{g} \pm 0.01 \text{g} \]. Therefore, the amount to measure is 10.01 grams (considering significant figures).

Precision of the Balance for Case (b)

The precision in case (b) is \( \pm 0.001 \text{g} \). This indicates the balance can measure within a range of 0.001 grams. With this precision: \[\text{Measured Amount for (b)} = 10.0123576 \text{g} \pm 0.001 \text{g} \]. Thus, the amount to measure is 10.012 grams (considering significant figures).

Precision of the Balance for Case (c)

The precision in case (c) is \( \pm 0.0001 \text{g} \). This allows the balance to measure within a range of 0.0001 grams. For this case: \[\text{Measured Amount for (c)} = 10.0123576 \text{g} \pm 0.0001 \text{g} \]. Therefore, the amount to measure is 10.0124 grams (considering significant figures).

Key concepts

Precision of Measurement

In any measurement, the precision of the instrument determines how close the repeated measurements of the same quantity are. When we talk about precision, we are referring to how detailed and exact the measurement can be given the instrument's limitations. For example, a balance with a precision of \(\text{±0.01 g}\) can measure weights to the nearest hundredth of a gram. If you need to measure \(\text{10.0123576 g}\) of NaCl, the precision of the balance will affect how accurately you can measure that value. Always note the range and be aware of the potential error margin when doing experiments. This helps ensure your results are not only accurate but also reliable.

NaCl Measurements

Sodium chloride, or NaCl, is a common compound that you might need to measure accurately in a chemistry lab. Proper measurement is critical in chemistry because even slight deviations can affect the outcome of an experiment. For this exercise, you're asked to calculate the exact amount of NaCl with varying degrees of precision from different balances. Each balance has a different error range, affecting how precisely you can measure the NaCl. For example:

• If the balance precision is \(\text{±0.01 g}\), the closest you can measure is \(\text{10.01 g}\).
• If the balance precision is \(\text{±0.001 g}\), you can get a more precise measurement like \(\text{10.012 g}\).
• If the balance precision is \(\text{±0.0001 g}\), it allows for the most precise measurement at \(\text{10.0124 g}\).

Understanding how precise your equipment is helps you know how to prepare for your experiments and achieve the desired results.

Significant Figures in Chemistry

Significant figures are the digits in a number that contribute to its precision. In chemistry, precise measurements are crucial, and significant figures help indicate the reliability of a measurement. For example, in the measurement \(\text{10.0123576 g}\):

• The digits \(\text{1, 0, 0, 1, 2, 3, 5, 7, 6}\) are all significant.
• The level of precision of an instrument affects how many significant figures you can report.

When you measure NaCl using a balance with different precisions:

• A balance with a precision of \(\text{±0.01 g}\) gives you \(\text{10.01 g}\), rounded to 4 significant figures.
• A balance with \(\text{±0.001 g}\) provides \(\text{10.012 g}\), showing 5 significant figures.
• A balance with \(\text{±0.0001 g}\) allows for a more detailed measurement like \(\text{10.0124 g}\), rounded to 6 significant figures.

Always consider significant figures when recording your data. It ensures that your measurements and calculations are as accurate as your equipment allows.