What is the density of nitrogen gas (molecular mass = 28 u) at a pressure of 1.2 atmospheres and a temperature of 284 K?
PV=nRT
PV= mass/molmass *RT
density= mass/volume
density= Pressure*molmassN2/RT
To find the density of nitrogen gas, you can use the ideal gas law equation:
PV = nRT
Where:
P is the pressure (in atmospheres)
V is the volume (in liters)
n is the number of moles
R is the ideal gas constant (0.0821 L·atm/(mol·K))
T is the temperature (in Kelvin)
First, let's rearrange the equation to solve for n/V (molar density) instead of PV:
n/V = P/RT
Now, we need to find the molar density of nitrogen gas. To do that, we'll need to convert the pressure and temperature to the correct units.
Given:
Pressure (P) = 1.2 atmospheres
Temperature (T) = 284 K
Now, plug in the values into the formula:
n/V = (1.2 atm) / (0.0821 L·atm/(mol·K) x 284 K)
Calculating this:
n/V = 0.044 mol/L
Since molecular mass (M) = 28 u, we know that:
1 mole of gas occupies M grams
0.044 moles of gas occupies (0.044 x M) grams
To convert grams into kilograms and liters to cubic meters, we need to know the density (D) formula:
Density (D) = mass/volume
Now, let's calculate the density:
D = (0.044 x M g) / (1 L x 1000 g/1 kg x 1000 L/1 m^3)
Substituting the value of M (molecular mass of nitrogen gas):
D = (0.044 x 28 g) / (1 L x 1000 g/1 kg x 1000 L/1 m^3)
Simplifying this:
D = 1.232 kg/m^3
So, the density of nitrogen gas at a pressure of 1.2 atmospheres and a temperature of 284 K is approximately 1.232 kg/m^3.
To find the density of a gas, we can use the ideal gas law equation, which states that the product of pressure and volume is directly proportional to the product of the number of moles, the gas constant, and the temperature. The equation is given as:
PV = nRT
where:
P = pressure (in atmospheres)
V = volume (in liters)
n = number of moles
R = gas constant (0.0821 L.atm/(mol.K))
T = temperature (in Kelvin)
In this case, we need to find the number of moles of nitrogen gas first. We can use the molecular mass of nitrogen to convert it to moles.
Molecular mass of nitrogen gas (N2) = 2 * molecular mass of nitrogen atom = 2 * 28u = 56u
Now, we can calculate the number of moles using the following formula:
n = mass / molecular mass
However, since we are given pressure and temperature, we assume that the gas behaves ideally, meaning we can use the ideal gas law directly to determine the number of moles. Rearranging the ideal gas law equation, we get:
n = PV / RT
Plugging in the given values:
P = 1.2 atm
V = unknown (we are finding density, not volume)
R = 0.0821 L.atm/(mol.K)
T = 284 K
n = (1.2 atm * V) / (0.0821 L.atm/(mol.K) * 284 K)
To find the density, we need to divide the mass of the gas by the volume occupied by the gas. The molecular mass of nitrogen gas (N2) is given as 28 u. The mass of the gas can be calculated by multiplying the number of moles of the gas by its molecular mass.
Density (ρ) = n * molecular mass / V
Plugging in the values, we have:
Density = (n * molecular mass) / V
To find the volume, we need to rearrange the equation for the ideal gas law. Since PV = nRT, we can rearrange it to solve for volume (V):
V = nRT / P
Substituting the value of density and rearranging the equation, we have:
Density = (n * molecular mass) / (nRT / P)
Simplifying the equation, we can cancel out n:
Density = (molecular mass * P) / RT
Now we can plug in the given values and calculate the density of nitrogen gas.
Density = (28u * 1.2 atm) / ((0.0821 L.atm/(mol.K)) * 284 K)
By simplifying and calculating the expression, we get the density of nitrogen gas.