If a soft-drink bottle whose volume is 1.50 is completely filled with water and then frozen to -10 , what volume does the ice occupy?
Water has a density of 0.997 at 25 ; ice has a density of 0.917 at -10 .
Could you also explain the steps as to how I would go about solving this problem or one like it?
If we say bottle is 1.5L, then
mass water = 1,500 mL x 0.997 g/mL = 1495.5 grams.
When frozen to -10,
volume = mass/density = 1495.5/0.917 = ?
1.5 WHAT?
Well, let's break the ice, I mean, the problem down step by step!
Step 1: Calculate the mass of the water.
Since the volume of the soft-drink bottle is 1.50 L and water has a density of 0.997 g/cm³ at 25°C, we can use the formula:
Mass = Density x Volume
Mass of water = 0.997 g/cm³ x 1500 cm³ = 1495.5 g
Step 2: Calculate the volume occupied by the ice.
Now we need to convert the mass of the water to the volume of the ice. Ice has a density of 0.917 g/cm³ at -10°C.
Volume of ice = Mass of water / Density of ice
Volume of ice = 1495.5 g / 0.917 g/cm³ ≈ 1630.61 cm³
So, the volume occupied by the ice is approximately 1630.61 cm³.
But hey, remember that I'm a Clown Bot, not an Ice Bot, so take my calculations with a grain of salt, or in this case, a chunk of ice!
To solve this problem, we need to calculate the volume occupied by the ice after freezing. Here are the steps:
Step 1: Find the mass of the water in the bottle:
Since the volume of the bottle is given as 1.50 L and water has a density of 0.997 g/mL at 25°C, we can calculate the mass of the water using the formula: Mass = Density x Volume.
Mass of water = 0.997 g/mL x 1.50 L = 1.4955 kg.
Step 2: Convert the temperature from -10°C to Kelvin:
To convert from Celsius to Kelvin, you need to add 273.15 to the given temperature.
Temperature in Kelvin = -10°C + 273.15 = 263.15 K.
Step 3: Find the volume of the ice:
As given, ice has a density of 0.917 g/mL at -10°C. We can use the formula: Volume = Mass / Density to find the volume of the ice.
Volume of ice = Mass of water / Density of ice = 1.4955 kg / (0.917 g/mL) = 1.631 L.
Hence, the volume occupied by the ice after freezing is approximately 1.631 liters.
To solve this problem, you need to understand the relationship between volume, density, and temperature. Here are the steps to calculate the volume of ice in your soft-drink bottle:
Step 1: Convert the temperature from Celsius to Kelvin.
- To do this, add 273.15 to the given temperature of -10 . Therefore, -10 + 273.15 = 263.15 K.
Step 2: Calculate the mass of water in the bottle.
- Use the equation: mass = volume x density.
- The volume of the soft-drink bottle is 1.50 L, and the density of water at 25 is 0.997 g/mL.
- Convert the volume to milliliters: 1.50 L x 1000 mL/L = 1500 mL.
- Now, calculate the mass: mass = 1500 mL x 0.997 g/mL.
Step 3: Calculate the volume of ice in the bottle.
- The density of ice at -10 is 0.917 g/mL.
- We need to find the volume, so rearrange the equation: volume = mass / density.
- First, convert the mass from grams to milliliters: mass x 1 mL / density.
- Now, calculate the volume: volume = mass / 0.917.
Step 4: Calculate the mass of ice in the bottle.
- Use the equation: mass = volume x density.
- The density of ice at -10 is still 0.917 g/mL, and the volume we calculated in Step 3.
- Calculate the mass: mass = volume x 0.917.
Step 5: Solve for the volume of ice by rearranging the mass equation:
- volume = mass / density.
- Substitute the value of mass calculated in Step 4 and the density of ice at -10 .
- Calculate the volume: volume = mass / 0.917.
Following these steps, you can find the volume of ice in the soft-drink bottle.