A sample of N20 gas has a density of 2.65 g/L at 298 K.
What must be the pressure of the gas (in mmHg )?
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To find the pressure of the gas, we need to use the ideal gas law equation, which is defined as:
PV = nRT
Where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.
First, we need to determine the number of moles of the N2O gas. To do that, we can use the equation:
density = mass/volume
Since the density is given as 2.65 g/L, we can assume that 1 L of the gas has a mass of 2.65 grams.
Next, we need to convert the mass of the gas to moles. We can use the molar mass of N2O to do that.
The molar mass of N2O is 28 grams/mole for N2 and 16 grams/mole for O, giving us a total molar mass of 44 grams/mole for N2O.
So, the number of moles of N2O gas can be calculated as follows:
moles = mass/molar mass = 2.65 g / 44 g/mol ≈ 0.060 moles
Now that we have the number of moles, we can solve for the pressure.
First, we need to convert the temperature from Kelvin to Celsius by subtracting 273.15.
298 K - 273.15 = 24.85 °C
We also need to convert the pressure to mmHg by multiplying by the factor of 760 (since 1 atm = 760 mmHg).
Now, let's plug in the values into the ideal gas law equation:
PV = nRT
P * 1 L = 0.060 moles * 0.0821 L.atm/mol.K * 24.85 °C
P = (0.060 * 0.0821 * 298) / 1
P = 1.16 atm
To convert atm to mmHg, we multiply by 760 mmHg/atm:
P = 1.16 atm * 760 mmHg/atm
P ≈ 882.8 mmHg
Therefore, the pressure of the N2O gas is approximately 882.8 mmHg.
To determine the pressure of the N2O gas in mmHg, you can use the ideal gas law equation: 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 in Kelvin.
Given:
Density of N2O gas = 2.65 g/L
Temperature (T) = 298 K
First, we need to calculate the molar mass of N2O (nitrous oxide). Nitrous oxide (N2O) has two nitrogen atoms (N) and one oxygen atom (O).
Nitrogen (N) has a molar mass of 14.01 g/mol, and oxygen (O) has a molar mass of 16.00 g/mol.
Molar mass of N2O = 2(14.01 g/mol) + 16.00 g/mol = 44.03 g/mol
Next, we need to calculate the number of moles (n) of N2O using the given density.
Density is defined as the mass (m) divided by the volume (V).
Density (ρ) = m/V
Here, we are given the density (ρ) as 2.65 g/L. Since density is mass per unit volume, we can say that 2.65 g/L is equal to 2.65 g of N2O in 1 liter (L).
Now, we need to convert the given density from grams per liter to grams per mole.
To do this, we divide the given density (in grams per liter) by the molar mass of N2O (in grams per mole).
2.65 g/L / 44.03 g/mol = 0.0601 mol/L
Now that we have the number of moles (n) per liter (L), we can substitute the values into the ideal gas law equation PV = nRT.
P = nRT / V
Substituting the values:
n = 0.0601 mol/L
R = 0.0821 L·atm/(mol·K) (the ideal gas constant)
T = 298 K
P = (0.0601 mol/L) * (0.0821 L·atm/(mol·K)) * (298 K) / 1 L
Simplifying the equation:
P = 1.807 atm
However, we need the pressure in mmHg, so we'll convert the pressure from atm to mmHg.
1 atm = 760 mmHg
P in mmHg = (1.807 atm) * (760 mmHg/1 atm)
P in mmHg = 1374 mmHg
Therefore, the pressure of the N2O gas is approximately 1374 mmHg.
P*molar mass = density*RT
Solve for P and convert to mm Hg.