Oxygen gas (O2(g)) has a density of 0.00111 g/cm3 at room temperature and 1 atmospheric pressure
. Oxygen gas (
) has a density of 0.00111 g/cm
at room temperature and 1 atmospheric pressure. If you had 1 gallon of pure oxygen gas, how much would that amount weigh in pounds? Hint: 1 gal = 3.78 L and 2.2 lbs = 1 kg. (13 points)
The Correct Answer and Explanation is:
To find the weight of 1 gallon of pure oxygen gas, we need to follow these steps:
Step 1: Convert the volume of oxygen from gallons to liters
We know that 1 gallon = 3.78 liters. So, the volume of oxygen gas we are dealing with is:Volume in liters=1 gallon×3.78 L/gallon=3.78 L\text{Volume in liters} = 1 \text{ gallon} \times 3.78 \text{ L/gallon} = 3.78 \text{ L}Volume in liters=1 gallon×3.78 L/gallon=3.78 L
Step 2: Use the density of oxygen gas to calculate the mass
The density of oxygen gas is given as 0.00111 g/cm³ at room temperature and 1 atm pressure. To proceed, we need to convert liters to cubic centimeters (cm³), since the density is given in g/cm³.
- 1 liter = 1000 cm³.
Thus, the volume of oxygen in cubic centimeters is:Volume in cm3=3.78 L×1000 cm3/L=3780 cm3\text{Volume in cm}^3 = 3.78 \text{ L} \times 1000 \text{ cm}^3/\text{L} = 3780 \text{ cm}^3Volume in cm3=3.78 L×1000 cm3/L=3780 cm3
Now, we can calculate the mass of oxygen using the formula:Mass=Density×Volume\text{Mass} = \text{Density} \times \text{Volume}Mass=Density×Volume
Substituting the values:Mass=0.00111 g/cm3×3780 cm3=4.1978 g\text{Mass} = 0.00111 \text{ g/cm}^3 \times 3780 \text{ cm}^3 = 4.1978 \text{ g}Mass=0.00111 g/cm3×3780 cm3=4.1978 g
So, the mass of 1 gallon of oxygen gas is approximately 4.20 grams.
Step 3: Convert grams to kilograms
Since 1 kilogram = 1000 grams, we convert the mass to kilograms:Mass in kg=4.20 g1000=0.0042 kg\text{Mass in kg} = \frac{4.20 \text{ g}}{1000} = 0.0042 \text{ kg}Mass in kg=10004.20 g=0.0042 kg
Step 4: Convert kilograms to pounds
Finally, we use the conversion factor: 1 kg = 2.2 lbs.Mass in lbs=0.0042 kg×2.2 lbs/kg=0.00924 lbs\text{Mass in lbs} = 0.0042 \text{ kg} \times 2.2 \text{ lbs/kg} = 0.00924 \text{ lbs}Mass in lbs=0.0042 kg×2.2 lbs/kg=0.00924 lbs
Final Answer:
The weight of 1 gallon of pure oxygen gas is approximately 0.00924 pounds.
Explanation:
The process involves converting the given volume (1 gallon) to liters, converting liters to cubic centimeters, using the density to calculate the mass in grams, and then converting grams to pounds. The small mass of oxygen gas illustrates how light gases can be compared to liquids or solids.
