An unknown gas at 25.1 ∘C and 1.00 atm has a molar mass of 16.04 g/mol. Assuming ideal behavior, what is the density of the gas?
Use P*molar mass = density*R*T
To find the density of the gas, we need to 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 (0.0821 L·atm/(K·mol)), and T is the temperature in Kelvin.
First, we need to convert the temperature from Celsius to Kelvin using the formula:
T(K) = T(°C) + 273.15.
So, T = 25.1 °C + 273.15 = 298.25 K.
Next, we rearrange the ideal gas law equation to solve for density, which is mass divided by volume:
PV = nRT
divide both sides by V:
P = (nRT) / V
Let's rearrange this equation again to solve for V:
V = (nRT) / P.
Since we are given the molar mass (16.04 g/mol) and assuming ideal behavior, we can determine the number of moles using the formula:
n = mass / molar mass.
Let's assume the mass of the gas sample is 1 gram:
n = 1 g / 16.04 g/mol = 0.0623 mol.
Now we can substitute the values into the equation for V:
V = (0.0623 mol) * (0.0821 L·atm/(K·mol)) * (298.25 K) / (1.00 atm).
Calculating this, we get:
V ≈ 1.856 L.
Finally, using the formula for density:
Density = mass / volume,
let's calculate the density of the gas:
Density = 1 g / 1.856 L,
which gives:
Density ≈ 0.539 g/L.
Therefore, the density of the gas at 25.1 °C and 1.00 atm is approximately 0.539 g/L.
To find the density of the gas, we first need to determine the number of moles of the gas using the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in L)
n = number of moles
R = ideal gas constant (0.0821 L.atm/mol.K)
T = temperature (in Kelvin)
Given:
P = 1.00 atm
T = 25.1 °C = 25.1 + 273.15 = 298.25 K
Rearranging the ideal gas law equation to solve for n:
n = PV / RT
n = (1.00 atm) x (V) / (0.0821 L.atm/mol.K) x (298.25 K)
Since the volume (V) is not given, we cannot calculate the number of moles of gas at this point. Therefore, we need additional information to proceed.
If we assume that the gas is at standard temperature and pressure (STP), where the pressure is 1 atm and the temperature is 0 °C or 273.15 K, we can calculate the number of moles:
n = (1.00 atm) x (V) / (0.0821 L.atm/mol.K) x (273.15 K)
Now, we need the molar mass of the gas to calculate the density. Given that the molar mass is 16.04 g/mol, we can determine the mass (m) of the gas using:
m = n x molar mass
Next, we need the volume of the gas in order to find its density. If the gas occupies a known volume (V), we can calculate the density (d) using the formula:
d = m / V
However, without knowing the volume (V) or additional information, we cannot determine the density of the gas.