$700 cm^3$ of gas was collected at a temperature of $30^{\circ}$ and pressure of 450 mmHg. Convert the volume of this gas to STP.
Answer (2)
Convert initial temperature from Celsius to Kelvin: T 1 = 30 + 273.15 = 303.15 K .
Convert final temperature from Celsius to Kelvin: T 2 = 0 + 273.15 = 273.15 K .
Apply the combined gas law: V 2 = P 2 T 1 P 1 V 1 T 2 .
Substitute the values and calculate the final volume: V 2 = ( 760 ) ( 303.15 ) ( 450 ) ( 700 ) ( 273.15 ) ≈ 373.46 c m 3 . The volume of the gas at STP is 373.46 c m 3 .
Explanation
Understanding the Problem We are given a volume of gas at a certain temperature and pressure, and we want to find the volume of the same gas at standard temperature and pressure (STP). We will use the combined gas law to solve this problem.
Gathering the Given Information First, let's list the given information:
Initial volume, V 1 = 700 c m 3
Initial temperature, T 1 = 3 0 ∘ C
Initial pressure, P 1 = 450 mm H g
We need to convert this gas to Standard Temperature and Pressure (STP), which is defined as:
Final temperature, T 2 = 0 ∘ C
Final pressure, P 2 = 760 mm H g
Our goal is to find the final volume, V 2 .
Converting Temperatures to Kelvin Before we use the combined gas law, we need to convert the temperatures from Celsius to Kelvin. Recall that T ( K ) = T ( ∘ C ) + 273.15 .
So, we have:
T 1 = 30 + 273.15 = 303.15 K
T 2 = 0 + 273.15 = 273.15 K
Applying the Combined Gas Law Now we can use the combined gas law, which is given by: T 1 P 1 V 1 = T 2 P 2 V 2 We want to solve for V 2 , so we rearrange the equation: V 2 = P 2 T 1 P 1 V 1 T 2
Calculating the Final Volume Now, we substitute the given values into the equation: V 2 = ( 760 mm H g ) ( 303.15 K ) ( 450 mm H g ) ( 700 c m 3 ) ( 273.15 K ) V 2 = 760 × 303.15 450 × 700 × 273.15 c m 3 V 2 = 230394 85985250 c m 3 V 2 ≈ 373.46 c m 3
Stating the Final Answer Therefore, the volume of the gas at STP is approximately 373.46 c m 3 .
Examples
Understanding how gases behave under different conditions is crucial in many real-world applications. For instance, in scuba diving, it's essential to know how the volume of air in a diver's tank changes with depth (pressure) and temperature to ensure they have enough air for the dive. Similarly, in weather forecasting, understanding how air masses change volume with temperature and pressure helps predict weather patterns. In industrial processes involving gases, such as chemical reactions or storage, knowing the volume changes under different conditions is vital for safety and efficiency. The combined gas law helps us make these predictions accurately.
Using the combined gas law, we calculated that the volume of gas collected at 30°C and 450 mmHg is approximately 373.46 cm³ when adjusted to standard temperature and pressure (STP). The calculations involved converting the initial temperatures to Kelvin and substituting values into the gas law equation. Therefore, the final volume of the gas at STP is about 373.46 cm³.
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