Question

PLEASE HELPPPP

Three samples of the same metal are weighed and their masses are found to be 37.31 g, 35.96 g, and 35.72 g. The corresponding volumes are 4.15 mL, 4.24 mL, and 4.02 mL, respectively. Determine the density, d, of the metal and calculate the standard deviation of the density.


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Answer 1

Explanation:

To determine the density, you can use the formula:

\[d = \frac{m}{V}\]

Where:

- \(d\) is the density

- \(m\) is the mass

- \(V\) is the volume

Let's calculate the density for each sample:

For the first sample: \(d_1 = \frac{37.31\, \text{g}}{4.15\, \text{mL}}\)

For the second sample: \(d_2 = \frac{35.96\, \text{g}}{4.24\, \text{mL}}\)

For the third sample: \(d_3 = \frac{35.72\, \text{g}}{4.02\, \text{mL}}\)

Now, calculate the mean (average) density:

\[\text{Mean density} = \frac{d_1 + d_2 + d_3}{3}\]

Next, calculate the standard deviation of the density. The formula for the sample standard deviation is:

\[s = \sqrt{\frac{\sum{(x_i - \bar{x})^2}}{n-1}}\]

Where:

- \(s\) is the standard deviation

- \(x_i\) are the individual densities

- \(\bar{x}\) is the mean density

- \(n\) is the number of samples (in this case, 3)

Now, calculate the standard deviation of the density using the above formula with the individual densities \(d_1\), \(d_2\), and \(d_3\), and the mean density.

Once you have these values, you'll have the density of the metal and its standard deviation.