Question

a scientist is determining the mass of 25,000 molecules of oxygen. use this to answer parts a and b. the mass of one molecule of oxygen = 5.3×10⁻²³ gram. a. how many significant digits should be in the solution? there should be 2 significant digits in the solution. (type a whole number.) b. express the mass of 25,000 molecules of oxygen in scientific notation. grams (type your answer using the appropriate number of significant digits. type your answer in scientific notation using the appropriate symbol from the math palette for any multiplication.)

Explanation:

Step1: Identify the number of significant digits in given values

The mass of one oxygen - molecule is $5.3\times10^{-23}$ gram (2 significant digits), and the number of molecules is 25000 (2 significant digits considering it's a measured or counted value for this context). In multiplication, the result should have the same number of significant digits as the value with the fewest significant digits among the values being multiplied.

Step2: Calculate the mass of 25000 molecules of oxygen

The mass of one molecule of oxygen is $m = 5.3\times10^{-23}$ gram, and the number of molecules $n=25000 = 2.5\times10^{4}$. The total mass $M=n\times m=(2.5\times10^{4})\times(5.3\times10^{-23})$. Using the rule of exponents $a^{m}\times a^{n}=a^{m + n}$, we have $M=(2.5\times5.3)\times10^{4+( - 23)}=13.25\times10^{-19}$. Adjusting to scientific - notation and 2 significant digits, $M = 1.3\times10^{-18}$ gram.

Answer:

$1.3\times10^{-18}$ grams