The density of hydrogen at STP is 0.09 g/l. What is the mass of the sample of hydrogen in exercise (36)
The Correct Answer and Explanation is:
To solve this question, we need to use the formula for density:Density=MassVolume\text{Density} = \frac{\text{Mass}}{\text{Volume}}Density=VolumeMass
This formula can be rearranged to solve for mass:Mass=Density×Volume\text{Mass} = \text{Density} \times \text{Volume}Mass=Density×Volume
From the information given:
- The density of hydrogen at STP is 0.09 g/L
- The volume of the hydrogen sample is taken from exercise (36), which states that three moles of hydrogen occupy 67.20 liters at STP
Now substitute the values into the equation:Mass=0.09 g/L×67.20 L\text{Mass} = 0.09 \, \text{g/L} \times 67.20 \, \text{L}Mass=0.09g/L×67.20LMass=6.048 g\text{Mass} = 6.048 \, \text{g}Mass=6.048g
Final Answer: 6.05 grams (rounded to two decimal places)
Explanation:
The concept of density relates how much mass of a substance is present in a given volume. In this case, we are given the density of hydrogen gas at standard temperature and pressure, which is 0.09 grams per liter. This value tells us that every liter of hydrogen gas weighs 0.09 grams under those conditions.
From a previous exercise, we know that three moles of hydrogen gas occupy 67.20 liters at STP. Because the density is in grams per liter, and we have the volume in liters, we can directly multiply the two to find the mass.
Multiplying the density by the volume gives the total mass of hydrogen gas in grams. The unit of liters cancels out during the multiplication, leaving the final result in grams.
This approach is widely used in chemistry to convert between mass and volume when the density is known. It is important to always check the units for consistency to ensure that the answer makes sense. In this example, both the units and the magnitude of the result are consistent with what we expect for a gaseous sample.
