If you have 0.985 g of CH4 gas at 98 °C and 855 mmHg, what volume would the gas occupy
To find the volume occupied by the gas, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atmospheres)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature (in Kelvin)
First, let's convert the temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 98 + 273.15 = 371.15 K
Next, let's convert the pressure from mmHg to atm:
P(atm) = P(mmHg) / 760
P(atm) = 855 mmHg / 760 = 1.125 atm
Now, we need to calculate the number of moles of CH4 gas using its molar mass:
CH4 molar mass = 12.011 g/mol (carbon) + 4 * 1.008 g/mol (hydrogen) = 16.043 g/mol
n = mass / molar mass
n = 0.985 g / 16.043 g/mol ≈ 0.0613 mol
Now, we can rearrange the ideal gas law equation to solve for V:
V = (nRT) / P
V = (0.0613 mol * 0.0821 L·atm/(mol·K) * 371.15 K) / 1.125 atm
Calculating:
V ≈ 1.55 L
Therefore, the gas would occupy approximately 1.55 liters.
To determine the volume the CH4 gas would occupy, we can use 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)
First, let's convert the given values to the proper units:
Mass of CH4 = 0.985 g
Temperature = 98 °C = (98 + 273) K
Pressure = 855 mmHg = (855 / 760) atm
Next, we need to find the number of moles of CH4 using its molar mass:
Molar mass of CH4 = 12.01 g/mol + 4 * 1.008 g/mol = 16.04 g/mol
Moles of CH4 = Mass of CH4 / Molar mass of CH4
= 0.985 g / 16.04 g/mol
Finally, we can substitute the values into the ideal gas law equation to solve for the volume:
PV = nRT
(V)(855/760) = (0.985 g / 16.04 g/mol)(0.0821 L·atm/(mol·K))(98 + 273 K)
Now we can solve for V:
V = [(0.985 g / 16.04 g/mol)(0.0821 L·atm/(mol·K))(98 + 273 K)] / (855/760)
Note: At this point, I would need the calculator to solve the equation and provide the final volume value.