#16 A gas occupies 7 L at 71.8 kPa & 30°C. Find its volume at 273K and 101.325 kPa. Show your work using the combined gas law.
#17 In the winter, bodies of water tend to not freeze solid. This allows fish and other aquatic life to survive below the floating ice. Explain the unique properties of water (high specific heat capacity and density) in the solid state as it relates to this situation.
#18 Explain why it takes longer to cook or bake certain foods at high altitudes compared to sea level.
16. Use PV = nRT. Convert pressure to atm (1 atm = 101.32 kPa) or use 8.314 for R.
17. I'll critique your answer. You know specific heat is high (almost higher than any other material) and you know density of ice is less than density of H2O at those temperatures.
18. Water boils at a lower temperature at elevated altitudes. It takes longer to cook something at 95 C than at 100 C.
Is the answer to Question 16: 184.2
Can you give me the answer to 17?
#16 To find the volume of the gas at the new conditions, we can use the combined gas law equation:
P1V1 / T1 = P2V2 / T2
Where:
P1 = initial pressure (71.8 kPa)
V1 = initial volume (7 L)
T1 = initial temperature in Kelvin (30°C + 273 = 303 K)
P2 = final pressure (101.325 kPa)
V2 = final volume (unknown)
T2 = final temperature in Kelvin (273 K)
First, let's convert the initial temperature to Kelvin:
T1 = 303 K
Now, we can substitute the values into the equation and solve for V2:
(71.8 kPa * 7 L) / (303 K) = (101.325 kPa * V2) / (273 K)
49.3 kPa L / K = 101.325 kPa * V2 / 273 K
Cross multiply:
49.3 kPa L * 273 K = 101.325 kPa * V2 * 303 K
13452.9 kPa L * K = 30700.275 kPa * V2
Divide both sides by 30700.275 kPa:
13452.9 kPa L * K / 30700.275 kPa = V2
V2 ≈ 0.437 L
Therefore, the volume of the gas at 273 K and 101.325 kPa is approximately 0.437 L.
#17 Water has unique properties in the solid state, which allow bodies of water to not freeze solid in the winter. These properties are high specific heat capacity and density.
High specific heat capacity means that water requires a relatively large amount of heat to raise its temperature compared to other substances. This property allows water to absorb a significant amount of heat energy without experiencing a significant temperature change. So, when the air temperature drops in winter, water can release heat to the surrounding environment, keeping the water temperature stable.
Density is another important property of water. Most substances become denser as they cool down. However, water is an exception. Water reaches its maximum density at around 4°C. As water cools below 4°C, its molecules organize in a way that increases the space between them, causing water to expand and become less dense. This expansion creates a layer of less dense water on top, insulating the denser water below and preventing it from freezing solid. This unique density behavior allows aquatic life to survive below the floating ice layer.
#18 Cooking or baking at high altitudes takes longer compared to sea level due to the reduced atmospheric pressure. At higher altitudes, there is lower air pressure, which affects the boiling point and cooking temperatures of foods.
The boiling point of water decreases as the atmospheric pressure decreases. At higher altitudes, where the air pressure is lower, water boils at temperatures lower than 100°C (212°F) at sea level. This reduced boiling point affects the cooking time for foods that require boiling, such as rice or pasta, as the lower temperature slows down the cooking process.
In baking, the reduced air pressure affects the leavening process. As the altitude increases, the air pressure decreases, resulting in gases (such as carbon dioxide) expanding more rapidly. This increased gas expansion causes baked goods to rise more quickly. However, the lower air pressure at high altitudes also affects the overall baking process. The lower pressure can cause baked goods to dry out faster due to increased evaporation, leading to longer cooking times.
To compensate for these factors, adjustments need to be made when cooking or baking at high altitudes. These adjustments may include increasing the cooking time, adjusting ingredient ratios, or using specific high altitude baking techniques to ensure desired results.