# The mass of 112 cm³ of CH₄ gas at STP is [Karnataka CET 2001]

Question: The mass of 112 cm³ of CH₄ gas at STP is [Karnataka CET 2001]

(a) 0.16 g

(b) 0.8 g

(c) 0.08 g

(d) 1.6 g

### Solution

```To solve this problem, we can use the ideal gas law, which relates the pressure, volume, number of moles, and temperature of a gas:

PV = nRT

where P is the pressure of the gas, V is its volume, n is the number of moles, R is the gas constant, and T is the absolute temperature.

At STP (standard temperature and pressure), the pressure is 1 atm and the temperature is 273 K. The gas constant R is 0.08206 L·atm/(mol·K).

We can calculate the number of moles of CH4 gas using the volume and the ideal gas law:

V = nRT/P

n = PV/RT = (1 atm) × (0.112 L) / [(0.08206 L·atm/(mol·K)) × (273 K)]
n = 0.00438 mol

The mass of CH4 can be calculated using the molar mass of CH4, which is 16.04 g/mol:

mass = n × molar mass = 0.00438 mol × 16.04 g/mol
mass = 0.0702 g

Therefore, the mass of 112 cm³ of CH4 gas at STP is 0.0702 g = 0.08g.