A quantity of N2 occupies a volume of 1 L at 290 K and 1.5 atm. The gas expands to a volume of 2.7 L as the result of a change in both temperature and pressure.
Find the density of the gas at these new conditions (in grams per liter).
same mass, so new density= old density/2.7
what is old density? You know pressure,volume, temp, find moles
PV=nRT
convert moles to grams.
Thank you, bobpursley! Got the answer - .653
Why did the gas go to a therapist?
Because it was feeling under pressure!
Now, let's calculate the density of the gas in the new conditions. To do that, we'll need to 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 we have a change in both temperature and pressure, we can use the combined gas law equation:
(P₁V₁) / (T₁) = (P₂V₂) / (T₂)
where P₁, V₁, and T₁ are the initial conditions and P₂, V₂, and T₂ are the final conditions.
Let's plug in the values we have:
P₁ = 1.5 atm
V₁ = 1 L
T₁ = 290 K
P₂ = P₁ (since it remains constant) = 1.5 atm
V₂ = 2.7 L
T₂ = unknown
Solving the combined gas law equation for T₂, we get:
T₂ = (P₂V₂T₁) / (P₁V₁)
Now that we have the final temperature, we can proceed to calculate the number of moles using the ideal gas law equation:
n = (PV) / (RT)
We already have the values for P, V, and T, so we can plug them in to find n.
Finally, to calculate the density, we need to know the molar mass of nitrogen gas (N₂). It is approximately 28 g/mol.
Density = (molar mass / Molar volume) = (molar mass / n)
Now, let's do the calculations and find the density of the gas!
To find the density of the gas at the new conditions, we need to determine the mass of the gas in grams and divide it by the volume in liters.
To calculate the mass, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure in atm
V = volume in liters
n = number of moles of gas
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature in Kelvin
We are given the initial conditions:
P1 = 1.5 atm
V1 = 1 L
T1 = 290 K
And the final conditions:
P2 = ?
V2 = 2.7 L
T2 = ?
First, we need to find the final pressure, P2. Since we know that the temperature and volume changed, we can use the combined gas law equation:
(P1 * V1) / T1 = (P2 * V2) / T2
Substituting the given values:
(1.5 atm * 1 L) / 290 K = (P2 * 2.7 L) / T2
Now we can solve for P2:
(1.5 L·atm) * T2 = (P2 * 2.7 L) * 290 K
P2 = ((1.5 atm * 1 L * 290 K) / (2.7 L))
Next, we need to calculate the number of moles, n. We can use the ideal gas law equation again:
n = (P * V) / (R * T)
Using the initial conditions:
n1 = (1.5 atm * 1 L) / (0.0821 L·atm/mol·K * 290 K)
And using the final conditions:
n2 = ((P2 * 2.7 L) / (0.0821 L·atm/mol·K * T2))
Finally, we can determine the mass of the gas using the formula:
Mass = n * Molar mass
Given that N2 is nitrogen gas, its molar mass is approximately 28 g/mol.
Now, we can calculate the mass of the gas at the new conditions:
Mass2 = n2 * 28 g/mol
Finally, to find the density, we divide the mass by the volume:
Density = Mass2 / V2
Plugging in the calculated values, we can find the density of the gas at the new conditions (in grams per liter).