If you have 0.985 g of CH4 gas at 98 °C and 855 mmHg, what volume would the gas occupy

Answer 1

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.