A 100-cm3 container has 4 g of ideal gas in it at 250 kPa. If the volume is changed to 50 cm3 and the temperature remains constant, what is its new density?
Answer
400 kg/m3
250 kg/m3
80 kg/m3
50 kg/m3
temp and pressure and so forth have NOTHING to do with what happens to the density here.
You STILL have 4 g in the container
before you had
4 g/100 cm^3 or .04 g /cc
now you have
4 g/50 cm^3 or .08 g/cc
80kg/m³
To find the new density of the gas, we can use the ideal gas law:
PV = nRT,
where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
Since the temperature remains constant, the ideal gas law can be rearranged to solve for the new density:
P1V1 = P2V2.
Here, P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.
Given:
Initial volume (V1) = 100 cm3
Final volume (V2) = 50 cm3
Initial pressure (P1) = 250 kPa
Now, we can calculate the final pressure (P2) using the formula:
P2 = (P1 * V1) / V2.
P2 = (250 kPa * 100 cm3) / 50 cm3 = 500 kPa.
Next, we can use the ideal gas law to find the number of moles of gas (n) in the container:
PV = nRT.
Since the temperature remains constant, the number of moles (n) remains constant as well.
Now, we can calculate the density (ρ) of the gas using the formula:
ρ = (n * M) / V,
where M is the molar mass of the gas.
Since the number of moles (n) and molar mass (M) remain constant, the formula simplifies to:
ρ ∝ 1 / V.
As the volume decreases, the density increases.
Therefore, the new density will be higher than the initial density of the gas. Among the given options, the answer is 400 kg/m3.
To find the new density of the gas when the volume is changed to 50 cm3, we need to use the ideal gas equation:
PV = nRT
where:
P = pressure of the gas
V = volume of the gas
n = number of moles of the gas
R = ideal gas constant
T = temperature of the gas
In this case, we are given the initial volume (100 cm3), initial pressure (250 kPa), and the fact that the temperature remains constant. We also know the number of moles of the gas can be determined using the ideal gas equation.
First, let's find the number of moles (n) of the gas:
PV = nRT
n = PV / RT
Given:
P = 250 kPa = 250,000 Pa (since 1 kPa = 1000 Pa)
V = 100 cm3 = 0.1 m3 (since 1 cm3 = 0.01 m3)
R = 8.314 J/(mol·K) (ideal gas constant)
T = constant (temperature)
n = (250,000 Pa * 0.1 m3) / (8.314 J/(mol·K) * T)
n = 30000 / T mol
Since the temperature remains constant, the number of moles (n) of the gas also remains constant.
Now that we have the number of moles of the gas, we can use it to find the new density when the volume is changed to 50 cm3. Density can be defined as the mass (m) of the gas divided by the volume (V) it occupies:
Density = m/V
We are given the mass of the gas initially (4 g) and the fact that the temperature and number of moles remain constant.
To find the new density, we need to find the new mass of the gas. Since the number of moles remains constant, the mass changes proportionally to the volume change:
Mass1 / Volume1 = Mass2 / Volume2
Given:
Mass1 = 4 g
Volume1 = 100 cm3 = 0.1 m3
Volume2 = 50 cm3 = 0.05 m3
Mass2 = (Mass1 * Volume2) / Volume1
Mass2 = (4 g * 0.05 m3) / 0.1 m3
Mass2 = 2 g
Now we can find the new density by dividing the new mass (2 g) by the new volume (50 cm3 = 0.05 m3):
Density = Mass2 / Volume2
Density = 2 g / 0.05 m3
Converting the units:
Density = (2 g) / (0.05 m3)
Density = 40 g/m3
So the new density of the gas when the volume is changed to 50 cm3 is 40 g/m3. However, the answer choices given are in kg/m3, which means we need to convert the unit:
Density = (40 g/m3) * (1 kg/1000 g)
Density = 0.04 kg/m3
Therefore, the answer is 0.04 kg/m3, which is equivalent to 40 kg/m3.