Which of the following can be used as valid conversion factors for a density of 2.5 g/ml?

• A. 2.5 g / 2.5 ml and 1 ml / 1 g
• B. 1 g / 2.5 ml and 2.5 ml / 1 g
• C. 2.5 g / 1 ml and 1 ml / 2.5 g
• D. 2.5 ml / 1 g and 1 g / 2.5 ml

Answer: (C)

Verified step by step guidance

1. Recall that density is defined as mass divided by volume, expressed as \(\text{density} = \frac{\text{mass}}{\text{volume}}\). For this problem, the density is given as 2.5 g/ml, meaning 2.5 grams per 1 milliliter.
2. To find valid conversion factors, remember that a conversion factor is a ratio equal to 1, which means the numerator and denominator represent the same quantity expressed differently but with the same value.
3. Using the density 2.5 g/ml, write two conversion factors: one with grams in the numerator and milliliters in the denominator, \(\frac{2.5\ g}{1\ ml}\), and the other with milliliters in the numerator and grams in the denominator, \(\frac{1\ ml}{2.5\ g}\). Both represent the same relationship and equal 1.
4. Check the options given to see which pairs correspond to these valid conversion factors. The pair must have one factor as \(\frac{2.5\ g}{1\ ml}\) and the other as \(\frac{1\ ml}{2.5\ g}\) to be correct.
5. Understand that options like \(\frac{1\ g}{2.5\ ml}\) or \(\frac{2.5\ ml}{1\ g}\) are not equivalent to the given density and thus cannot be used as valid conversion factors.