Ethylene glycol, an antifreeze. has a density of 1.11 g/mL at 20 °C.
a) What is the mass, in grams of 452 mL ethylene glycol?
b) What is the mass in kilograms of 18.6 L ethylene glycol?
c) What is the volume, in milliliters, occupied by 65.0 g ethylene glycol?
The Correct Answer and Explanation is :
To solve these problems, we can use the basic density equation:
[
\text{Density} = \frac{\text{Mass}}{\text{Volume}}
]
This can be rearranged to solve for mass, volume, or density depending on the given information:
[
\text{Mass} = \text{Density} \times \text{Volume}
]
[
\text{Volume} = \frac{\text{Mass}}{\text{Density}}
]
Given the density of ethylene glycol as 1.11 g/mL at 20 °C, we can now proceed with each part of the question.
a) What is the mass in grams of 452 mL of ethylene glycol?
We are given the volume (452 mL) and the density (1.11 g/mL), so we can use the formula for mass:
[
\text{Mass} = 1.11 \, \text{g/mL} \times 452 \, \text{mL} = 501.72 \, \text{g}
]
So, the mass of 452 mL of ethylene glycol is 501.72 grams.
b) What is the mass in kilograms of 18.6 L of ethylene glycol?
First, we need to convert the volume from liters to milliliters (1 L = 1000 mL). So:
[
18.6 \, \text{L} = 18.6 \times 1000 = 18,600 \, \text{mL}
]
Now we can calculate the mass using the density formula:
[
\text{Mass} = 1.11 \, \text{g/mL} \times 18,600 \, \text{mL} = 20,646 \, \text{g}
]
To convert grams to kilograms (1 kg = 1000 g):
[
\text{Mass} = \frac{20,646 \, \text{g}}{1000} = 20.646 \, \text{kg}
]
So, the mass of 18.6 L of ethylene glycol is 20.646 kilograms.
c) What is the volume in milliliters occupied by 65.0 g of ethylene glycol?
We are given the mass (65.0 g) and the density (1.11 g/mL), and we need to solve for the volume. Using the formula for volume:
[
\text{Volume} = \frac{\text{Mass}}{\text{Density}} = \frac{65.0 \, \text{g}}{1.11 \, \text{g/mL}} = 58.65 \, \text{mL}
]
So, the volume occupied by 65.0 g of ethylene glycol is 58.65 milliliters.
Summary:
- a) 452 mL ethylene glycol has a mass of 501.72 grams.
- b) 18.6 L ethylene glycol has a mass of 20.646 kilograms.
- c) 65.0 g of ethylene glycol occupies 58.65 milliliters.
These calculations are based on applying the density formula, using unit conversions when necessary, and ensuring consistent units throughout the problem.