Calculate no. of moles of hydrogen gas present in 0.5dm^3 sample of hydrogen gas at pressure of 101.325kpa and at the temperature of 27`c

To determine the number of moles of hydrogen gas in a given volume under specific conditions, we can use the Ideal Gas Law, which is expressed as PV = nRT. In this equation, P represents the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin. Let’s break this down step by step.

Step 1: Convert Temperature to Kelvin

The temperature needs to be in Kelvin for the Ideal Gas Law. The conversion from Celsius to Kelvin is done by adding 273.15.

• Temperature in Celsius: 27°C
• Temperature in Kelvin: 27 + 273.15 = 300.15 K

Step 2: Convert Pressure to Atmospheres

The pressure should also be in the correct units. The standard unit for pressure in the Ideal Gas Law is atmospheres (atm). To convert kilopascals (kPa) to atmospheres, we can use the conversion factor: 1 atm = 101.325 kPa.

• Pressure in kPa: 101.325 kPa
• Pressure in atm: 101.325 kPa / 101.325 = 1 atm

Step 3: Use the Ideal Gas Law

Now that we have all the necessary values, we can substitute them into the Ideal Gas Law equation. The ideal gas constant R is typically 0.0821 L·atm/(K·mol).

• P (pressure) = 1 atm
• V (volume) = 0.5 dm³ = 0.5 L
• T (temperature) = 300.15 K
• R (ideal gas constant) = 0.0821 L·atm/(K·mol)

Step 4: Rearranging the Ideal Gas Law

We need to solve for n (the number of moles), so we rearrange the equation:

n = PV / RT

Step 5: Plugging in the Values

Now we can substitute the values into the equation:

n = (1 atm) * (0.5 L) / (0.0821 L·atm/(K·mol) * 300.15 K)

Step 6: Performing the Calculation

Calculating the denominator first:

• 0.0821 L·atm/(K·mol) * 300.15 K ≈ 24.726

Now substituting back into the equation:

n = 0.5 / 24.726 ≈ 0.0202 moles

Final Result

Therefore, the number of moles of hydrogen gas present in the 0.5 dm³ sample at the given conditions is approximately 0.0202 moles.