Calculating the Mass of 12 cc of Hydrogen Gas at STP

To find the mass of 12 cubic centimeters (cc) of hydrogen gas under standard temperature and pressure (STP), we can use the principles of the ideal gas law and molar mass. This guide will walk you through the steps and present different methods to achieve the same result accurately.

Understanding STP

Standard Temperature and Pressure (STP) are conditions defined for the ideal gas law, where the temperature is 0°C (273.15 K) and the pressure is 1 atmosphere (1 atm). At these conditions, 1 mole of any ideal gas occupies 22.4 liters (22,400 cc).

Step-by-Step Calculation Using Molar Mass

Conversion of Volume

First, we convert the volume from cubic centimeters to liters:

[ 12 , text{cc} 0.012 , text{liters} ]

Calculation of Moles

To calculate the number of moles of hydrogen gas, we use the formula that relates volume, molar volume, and moles:

[ text{Number of moles} frac{text{Volume at STP}}{text{Molar volume}} frac{0.012 , text{liters}}{22.4 , text{liters/mole}} approx 0.000536 , text{moles} ]

Calculation of Mass

The mass of the hydrogen gas can be calculated by multiplying the number of moles by the molar mass of hydrogen gas (2 grams per mole):

[ text{Mass} text{Number of moles} times text{Molar mass} 0.000536 , text{moles} times 2 , text{g/mole} approx 0.001072 , text{grams} ]

Using the Ideal Gas Law

Ideal Gas Law Formula

The ideal gas law is given by:

[ PV nRT ]

Where:

P is the pressure in atmospheres (atm) V is the volume in liters (L) n is the number of moles R is the universal gas constant (0.082056 L·atm/(mol·K)) T is the temperature in Kelvin (K)

Application of Ideal Gas Law at STP

At STP, the conditions are:

P 1 atm V 12 ml 0.012 L T 273 K

Substitute these values into the ideal gas law formula to find the number of moles:

[ 1 , text{atm} times 0.012 , text{L} n times 0.082056 , text{L·atm/(mol·K)} times 273 , text{K} ]

Solving for n:

[ n frac{1 times 0.012}{0.082056 times 273} approx 0.0005356 , text{moles} ]

Since hydrogen gas exists as a diatomic molecule, the molar mass of hydrogen gas is 2 grams per mole. Therefore, the mass can be calculated as:

[ text{Mass} 0.0005356 , text{moles} times 2 , text{g/mole} approx 0.0010712 , text{grams} ]

Using Density

Density of Hydrogen Gas at STP

The density of hydrogen gas at STP is approximately 0.0899 grams per liter (g/L). Therefore, the mass of 12 cc (0.012 L) of hydrogen gas can be found by multiplying the density by the volume:

[ text{Mass} 0.0899 , text{g/L} times frac{12 , text{cc}}{1000 , text{cc/L}} 1.0788 times 10^{-3} , text{grams} ]

Conclusion

The mass of 12 cc of hydrogen gas at STP, using different methods, is approximately:

0.001072 grams (using molar mass and volume conversion) 0.0010712 grams (using the ideal gas law) 0.0010788 grams (using the density of hydrogen gas at STP)

Note that there can be minor differences due to rounding errors or the use of different constants such as the value of the universal gas constant (R).

Additional Information

Hydrogen gas at STP is a common reference for standard conditions in chemistry and physics. Understanding and applying the ideal gas law, as well as knowing the molar mass and density of gases, are fundamental skills in these fields.