at what temperature will nitrogen gas have a density of 1.13 grams/meters at a pressure of 1.09 ATM
PM = density*R*T
M = molar mass
To determine the temperature at which nitrogen gas will have a density of 1.13 grams/meters at a pressure of 1.09 ATM, we can use the ideal gas law formula:
PV = nRT
where:
P = pressure (in ATM)
V = volume (in meters)
n = number of moles
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature (in Kelvin)
First, we need to convert the given density from grams/meters to grams/liters, as the units in the ideal gas law equation need to be consistent.
1 meter = 100 centimeters = 1000 millimeters
1 liter = 1000 cubic centimeters
Thus, 1 gram/meter = 1 gram / (1000 cubic centimeters) = 0.001 grams/liter.
Therefore, the given density of 1.13 grams/meter is equivalent to 0.00113 grams/liter.
Now, let's rearrange the ideal gas law equation to isolate T:
T = PV / (nR)
We know:
P = 1.09 ATM
V = 1 liter (since we converted density to grams per liter)
n = unknown (we will solve for it)
Next, we need to determine the number of moles (n). We can use the molar mass of nitrogen, which is approximately 28 grams/mol.
n = mass / molar mass
n = density x volume / molar mass
n = 0.00113 grams/liter x 1 liter / 28 grams/mol
n ≈ 4.04 x 10^-5 mol
Now, substitute the known values into the equation:
T = (1.09 ATM) x (1 liter) / (4.04 x 10^-5 mol) x (0.0821 L·atm/(mol·K))
T ≈ 274 Kelvin
Therefore, the nitrogen gas will have a density of 1.13 grams/meters at a temperature of approximately 274 Kelvin.
To find the temperature at which nitrogen gas will have a density of 1.13 grams/meter³ at a pressure of 1.09 ATM, you need to use the Ideal Gas Law equation, which relates the pressure (P), volume (V), temperature (T), and the number of moles of gas (n).
The Ideal Gas Law equation is:
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)
In this particular question, we are given the pressure (P = 1.09 ATM) and the desired density (density = 1.13 g/m³). However, we need to convert the density into moles per liter before proceeding with the calculations.
To convert grams/meter³ to moles/Liter, we need to know the molar mass of nitrogen gas. The molar mass of nitrogen (N₂) is approximately 28 g/mol.
Now, let's calculate the number of moles per liter (n/V):
1. Convert density from grams/meter³ to grams/Liter:
- Since there are 1000 liters in a cubic meter, the density becomes 1.13 grams/Liter.
2. Convert grams/Liter to moles/Liter:
- Divide the grams/Liter by the molar mass of nitrogen (28 g/mol). Therefore, the result is 1.13 g/L / 28 g/mol = 0.0404 mol/L.
Now that we have the number of moles per liter, we can rearrange the Ideal Gas Law equation to solve for temperature:
PV = nRT
Rearranging the equation to solve for temperature (T):
T = PV / (nR)
Plugging in the given values:
T = (1.09 ATM) * V / (0.0404 mol/L * 0.0821 L·atm/(mol·K))
Now, you need to know the volume (V) at which you want to calculate the temperature. Please provide the volume or specify if it is at constant volume (V) or constant pressure (1.09 ATM).