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 measurements. 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. Additionally, the pressure at STP is set at 1 atmosphere (atm). Therefore, when referring to STP, remember that it signifies a temperature of 273.15 K and a pressure of 1 atm, which are essential for accurately applying gas laws and performing calculations in chemistry.

To determine the mass of oxygen gas present in a sample with a volume of 325 mL at standard temperature and pressure (STP), we can utilize the ideal gas law. 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 in liters (0.325 L)
• R = ideal gas constant (0.08206 L·atm/(mol·K))
• T = temperature in Kelvin (273.15 K)

First, convert the volume from milliliters to liters:

$$ V = 325 \, \text{mL} = 0.325 \, \text{L} $$

Next, substitute the values into the equation to find the number of moles:

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

Calculating this gives:

$$ n \approx 0.01450 \, \text{moles of } O_2 $$

To convert moles to grams, use the molar mass of oxygen gas (O₂), which is 32 grams per mole:

$$ \text{mass} = n \times \text{molar mass} $$

$$ \text{mass} = 0.01450 \, \text{moles} \times 32 \, \text{g/mol} $$

This results in:

$$ \text{mass} \approx 0.464 \, \text{grams of } O_2 $$

When considering significant figures, the final answer should reflect three significant figures, resulting in:

$$ \text{mass} \approx 0.464 \, \text{grams of } O_2 $$

In summary, by applying the ideal gas law and converting moles to grams, we find that a sample of oxygen gas with a volume of 325 mL at STP contains approximately 0.464 grams of O₂.

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 moles cancel out, and we can simplify the equation to find the volume:

V = \frac{RT}{P}

Substituting the values for R (0.0821 L·atm/(K·mol)), T (273.15 K), and P (1 atm), we find that the volume is:

V = 0.0821 \cdot 273.15 / 1 = 22.4 \text{ liters}

This result indicates that the standard molar volume of an ideal gas at STP is 22.4 liters. This value serves as a vital conversion factor, allowing for the conversion between moles and volume for any ideal gas under these conditions. Therefore, whenever dealing with 1 mole of an ideal gas at STP, one can confidently use the standard molar volume of 22.4 liters.

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 principles of gas laws.

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 of Cl₂ as follows:

Given:

Volume (V) = 15.7 liters

Conversion factor = 1 mole / 22.4 liters

Calculating moles:

moles = 15.7 liters × (1 mole / 22.4 liters) = 0.701 moles of Cl₂

The second method employs the ideal gas law, represented by the equation:

PV = nRT

Where:

• P = pressure (1 atmosphere at STP)
• V = volume (15.7 liters)
• n = number of moles
• R = ideal gas constant (0.0821 L·atm/(K·mol))
• T = temperature (273.15 K at STP)

Rearranging the equation to solve for n gives:

n = PV / RT

Substituting the known values:

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

Calculating this yields:

n ≈ 0.701 moles of Cl₂

Both methods yield the same result, demonstrating that we can determine the number of moles of a gas at STP either through the standard molar volume or by applying the ideal gas law. Understanding these approaches is essential for solving gas-related problems in chemistry.