Question

Find the length of magnesium metal ribbon that remains after two \(25.0-\mathrm{cm}\) strips are cut from \(255 \mathrm{~cm}\) of the ribbon.

Short answer

The remaining length of the magnesium ribbon is 205.0 cm.

Step-by-step solution

Determine the Total Length of Magnesium Ribbon Cut

First, identify the length of each strip cut from the ribbon. Since two strips of length 25.0 cm each are cut, calculate the total length of the ribbon that has been removed by multiplying the number of strips by the length of each strip. \[\text{Total length cut} = 2 \times 25.0 \text{ cm} = 50.0 \text{ cm}\]

Calculate the Remaining Length of the Ribbon

Subtract the total length of the ribbon cut from the original length of the magnesium ribbon to find out how much of the ribbon remains:\[\text{Remaining length} = 255 \text{ cm} - 50.0 \text{ cm} = 205.0 \text{ cm}\]

Key concepts

Length Measurements in Chemistry

In chemistry, precise measurements are critical to ensure accurate experimental results and data analysis. When discussing length measurements, the magnesium ribbon problem offers a clear example. Here, lengths are presented in centimeters, a standard unit of measurement in chemistry that allows for consistency and clarity across experiments and calculations.

• **Unit of Measurement:** Centimeters (cm) are commonly used for small length measurements in chemistry due to their precision and ease of use in lab settings.
• **Importance of Consistency:** Using the same units across measurements ensures that your calculations are correct and converts are unnecessary.
• **Precision:** Noting the precision (number of decimal places) is crucial, as it reflects the measurement accuracy.

When dealing with materials like the magnesium ribbon, knowing exactly how much material is used or remains can impact chemical reactions and outcomes significantly. Proper measurement units align with SI units, enhancing worldwide collaborative research and understanding.

Mathematical Operations in Chemistry

Math is integral to chemistry, particularly for quantitative analysis. This problem demonstrates a basic yet essential mathematical operation: multiplication.

• **Determining Total Quantity:** When cutting two strips of magnesium, each measuring 25.0 cm, multiplication helps calculate the total length removed.
• **Formula Application:** The formula \(\text{Total Length Cut} = \text{Number of Strips}\times\text{Length of Each Strip}\) is applicable here.
• **Accuracy in Calculations:** Ensure numbers retain their measurement units during calculations to maintain clarity and prevent errors.

Understanding and executing mathematical operations precisely is vital across various chemical applications, such as calculating concentrations, reaction yields, or material lengths. As in this case, every operation must reflect the problem's context to maintain scientific accuracy.

Subtraction in Problem Solving

Subtraction is a straightforward yet powerful tool in problem-solving, especially in cases like determining what's left after a process. In this exercise, subtraction is employed to find the length of magnesium ribbon remaining.

• **Initial vs. Remaining:** By subtracting the total length cut from the original, you obtain the length that remains (\(255 \text{ cm} - 50.0 \text{ cm} = 205.0 \text{ cm}\)).
• **Significance in Chemistry:** Knowing leftovers or remaining amounts ensures correct proportions in experiments, important for safety and efficacy.
• **Zeroing Errors:** Double-checking calculations for subtraction reduces errors, crucial when dealing with significant figures or sensitive data.

In chemistry, precise subtraction can mean the difference between success and failure in an experiment, making it essential to master this basic operation.