A student collects 500 cm^3 of methane gas at STP. Determine the moles of gas present, the number of methane molecules and the mass of methane.

Answer 1

Methane gas = CH₄

Molar mass = 16 g / mole

Since the problem states the conditions are at STP, we can use a short cut around the Ideal gas law.

We can use the fact that 1 mole of an ideal gas at STP = 22.4 Liters.

500 cm³ x 1 L / 1000 cm³ = 0.500 L

0.500 L x 1 mol / 22.4 L = 0.022 mols CH₄

Mass of CH₄ = 0.022 mols x 16 g / mol = 0.35 g CH₄

Molecules of CH₄ = 0.022 mols x 6.022x10²³ molecules / mole = 1.3x10²² molecules

Answer 2

STP stands for Standard Temperature and Pressure, which is defined as a temperature of 0°C (273.15 K) and a pressure of 1 atm (101.325 kPa).

To determine the number of moles of methane gas present, we can use the ideal gas law, which relates the pressure (P), volume (V), number of moles (n), and temperature (T) of a gas:

PV = nRT

where R is the ideal gas constant, which has a value of 0.0821 L·atm/mol·K.

At STP, the pressure is 1 atm and the temperature is 273.15 K. Therefore, we can calculate the number of moles of methane as:

n = PV/RT = (1 atm) x (500 cm^3/1000 cm^3/L) / (0.0821 L·atm/mol·K) x (273.15 K) = 0.0202 moles

To determine the number of methane molecules present, we can use Avogadro's number, which is the number of particles in one mole of a substance, and has a value of 6.022 x 10^23 particles/mol. Therefore, the number of methane molecules is:



N = n x N_A = 0.0202 moles x 6.022 x 10^23 particles/mol = 1.22 x 10^22 molecules

Answer 3

To determine the moles of methane gas present, we can use the ideal gas law: 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.

At STP (Standard Temperature and Pressure), P = 1 atm and T = 273 K. The volume is given as 500 cm^3, which is equivalent to 0.5 L. The gas constant R is 0.0821 L·atm/mol·K.

Using these values, we can solve for n:

n = PV/RT = (1 atm) × (0.5 L) /(0.0821 L·atm/mol·K × 273 K) = 0.0202 mol

Therefore, there are 0.0202 moles of methane gas present.

To determine the number of methane molecules, we can use Avogadro's number, which is the number of particles (atoms, molecules, etc.) in one mole of substance. Avogadro's number is approximately 6.022 × 10^23 particles/mol.

The number of methane molecules is therefore:(0.0202 mol) × (6.022 × 10^23 molecules/mol) = 1.22 × 10^22 molecules

To determine the mass of methane, we can use the molar mass of methane, which is 16.04 g/mol. The mass of methane is therefore:

(0.0202 mol) × (16.04 g/mol) = 0.324 g

Therefore, the student has 0.0202 moles of methane gas, which is equivalent to 1.22 × 10^22 methane molecules .