1) what is the density of methane (CH4) at a temp. of 20C and a pressure of 684mm.
2) a gas has a density of 2.5g/L at a temp. of 20C and a pressure of 1.1 atm. what is its molar mass.
I use the modified ideal gas equation for that. PM = dRT
M = molar mass
d = density
T must be in kelvin
To answer both of these questions, we can use the ideal gas law, which relates the pressure, volume, temperature, and number of moles of a gas. The ideal gas law equation is:
PV = nRT
where:
P = pressure of the gas
V = volume of the gas
n = number of moles of the gas
R = ideal gas constant (0.0821 L•atm/(mol•K))
T = temperature of the gas in Kelvin
To solve these questions, we'll need to convert the given temperature and pressure values to Kelvin and atm, respectively. Then we can use the ideal gas law to find the missing value: density or molar mass.
Let's solve each question step by step:
1) Density of methane (CH4) at a temperature of 20°C and a pressure of 684 mmHg:
- Convert the temperature to Kelvin: 20°C + 273.15 = 293.15 K
- Convert the pressure to atm: 684 mmHg / 760 mmHg/atm = 0.9 atm
Now we have the temperature (T = 293.15 K) and pressure (P = 0.9 atm). We need to determine the density.
To calculate the density (ρ), we need the molar mass (M) of methane (CH4). The molar mass of CH4 is 16.04 g/mol.
The ideal gas law equation rearranges to:
PV = nRT
(P / RT) = n / V
Density is defined as mass divided by volume:
ρ = m / V
Since the molar mass (M) is equal to the mass (m) divided by the number of moles (n):
M = m / n
Combining these equations, we have:
M = ρRT / P
Plugging in the values:
M = (density in g/L * 0.0821 L•atm/(mol•K) * 293.15 K) / 0.9 atm
2) A gas has a density of 2.5 g/L at a temperature of 20°C and a pressure of 1.1 atm:
- Convert the temperature to Kelvin: 20°C + 273.15 = 293.15 K
- Pressure is already given as 1.1 atm
Now we have the temperature (T = 293.15 K) and pressure (P = 1.1 atm). We need to determine the molar mass.
Using the same equation as above:
M = ρRT / P
Plugging in the values:
M = (2.5 g/L * 0.0821 L•atm/(mol•K) * 293.15 K) / 1.1 atm
Now that we have the equations and calculations for both questions, you can substitute the values and solve for the molar mass or density using a calculator.