Standard Temperature and Pressure: Videos & Practice Problems

Standard temperature and pressure (STP) is a crucial concept in gas calculations, providing a reference point for various scientific applications. At STP, the temperature is defined as 0 degrees Celsius, which is equivalent to 273.15 Kelvin. It is important to use Kelvin for gas calculations, as it is the absolute temperature scale. The pressure at STP is set at 1 atmosphere (atm). Therefore, when referring to STP, remember that it signifies a temperature of 273.15 Kelvin and a pressure of 1 atmosphere, which are essential for accurate gas law calculations.

To determine the mass of oxygen gas from a given volume at standard temperature and pressure (STP), we can utilize the ideal gas law. The problem states that a sample of oxygen gas has a volume of 325 mL at STP. First, we need to convert the volume from milliliters to liters, which gives us 0.325 L.

At STP, the pressure is 1 atmosphere and the temperature is 273.15 Kelvin. The ideal gas law can be expressed as:

\[n = \frac{PV}{RT}\]

Where:

• n = number of moles
• P = pressure (1 atm)
• V = volume (0.325 L)
• R = ideal gas constant (0.08206 L·atm/(mol·K))
• T = temperature (273.15 K)

Substituting the known values into the equation, we calculate the number of moles of oxygen gas:

\[n = \frac{(1 \, \text{atm})(0.325 \, \text{L})}{(0.08206 \, \text{L·atm/(mol·K)})(273.15 \, \text{K})}\]

After performing the calculation, we find that:

\[n \approx 0.01450 \, \text{moles of } O_2\]

Next, to convert moles to grams, we use the molar mass of oxygen. The molar mass of O₂ is 32 grams per mole (since each oxygen atom has a mass of approximately 16 grams, and there are two atoms in a molecule of O₂). Thus, the conversion is straightforward:

\[\text{mass} = n \times \text{molar mass} = 0.01450 \, \text{moles} \times 32 \, \text{g/mol} \approx 0.464 \, \text{grams of } O_2\]

Finally, rounding to three significant figures (as indicated by the original volume of 325 mL), the mass of the oxygen gas is approximately 0.464 grams. This process illustrates the relationship between volume, moles, and mass in gas calculations, emphasizing the importance of unit conversions and the ideal gas law in determining the properties of gases under specific conditions.

In the context of standard temperature and pressure (STP), the concept of standard molar volume is crucial for understanding the behavior of gases. Standard molar volume refers to the volume occupied by one mole of an ideal gas at STP, which is defined as a temperature of 273.15 Kelvin and a pressure of 1 atmosphere.

The relationship between volume, moles, and the ideal gas law can be expressed with the formula:

V = n \cdot \frac{RT}{P}

In this equation, V represents volume, n is the number of moles, R is the ideal gas constant, T is the temperature in Kelvin, and P is the pressure in atmospheres. When we consider 1 mole of an ideal gas at STP, the equation simplifies as the units for moles, temperature, and pressure cancel out, leading to a volume of:

22.4 \text{ liters}

This value, 22.4 liters, is significant as it establishes a direct conversion factor: for any ideal gas at STP, one mole will occupy 22.4 liters. This relationship is essential for calculations involving gas volumes and moles, allowing for straightforward conversions in stoichiometric calculations and gas law applications.

To determine the number of moles of chlorine gas (Cl₂) occupying a volume of 15.7 liters at standard temperature and pressure (STP), we can utilize two different methods based on the properties of ideal gases.

The first method involves using the standard molar volume of an ideal gas, which is 22.4 liters per mole at STP. By applying this conversion factor, we can calculate the moles as follows:

Number of moles (n) = Volume (V) / Molar volume = 15.7 L / 22.4 L/mol

When we perform this calculation, we find:

n = 0.70 moles of Cl₂

Alternatively, we can use the ideal gas law, represented by the equation:

PV = nRT

In this equation, P is the pressure (1 atmosphere at STP), V is the volume (15.7 liters), n is the number of moles, R is the ideal gas constant (0.0821 L·atm/(K·mol)), and T is the temperature (273.15 K at STP). Rearranging the equation to solve for n gives us:

n = PV / RT

Substituting the known values:

n = (1 atm) * (15.7 L) / (0.0821 L·atm/(K·mol) * 273.15 K)

After performing this calculation, we also arrive at:

n = 0.70 moles of Cl₂

Both methods yield the same result, demonstrating that we can approach gas calculations using either the standard molar volume or the ideal gas law, depending on the information available.