Question

how many atoms of p are present when a p₂o₅ sample contains 5.2 × 10²³ atoms o? path : atoms o → atoms p internal ratio = ? × 10^? atoms p hint: which internal ratio correctly allows the units to cancel? (5 atom o)/(2 atom p) or (2 atom p)/(5 atom o)

Explanation:

Step1: Identify the mole ratio

In \( \text{P}_2\text{O}_5 \), the ratio of P atoms to O atoms is \( \frac{2 \text{ atoms P}}{5 \text{ atoms O}} \). This ratio will be used to convert atoms of O to atoms of P.

Step2: Set up the conversion

We have \( 5.2 \times 10^{23} \) atoms of O. Multiply this by the ratio \( \frac{2 \text{ atoms P}}{5 \text{ atoms O}} \) to cancel out the O atoms and get P atoms.

\[
5.2 \times 10^{23} \text{ atoms O} \times \frac{2 \text{ atoms P}}{5 \text{ atoms O}}
\]

Step3: Perform the calculation

First, calculate the coefficient: \( \frac{5.2 \times 2}{5} = \frac{10.4}{5} = 2.08 \)

Then, the exponent remains \( 10^{23} \) (since we're only multiplying by a constant factor, not changing the power of 10).

So, the number of P atoms is \( 2.08 \times 10^{23} \)

Answer:

\( 2.08 \times 10^{23} \) atoms P (So the green box is 2.08 and the yellow box is 23)