The total volume of seawater is 1.5 times 10 to the twenty- first power L. Assume that seawater contains 3.1 percent sodium chloride by mass and that it's density is 1.03 g/mL. Calculate the total mass of sodium chloride in kilograms and in tons. ( 1 ton = 2000 lb. ; 1 lb. = 453.6 g. )
To calculate the total mass of sodium chloride in kilograms, we need to find the volume of seawater in milliliters (mL) and then convert it to grams (g) using the density of seawater. Finally, we can calculate the mass of sodium chloride in grams and convert it to kilograms.
Given:
Total volume of seawater = 1.5 × 10^21 L
Density of seawater = 1.03 g/mL
Sodium chloride concentration = 3.1% (by mass)
Step 1: Convert the volume of seawater to milliliters (mL)
1 L = 1000 mL
Total volume of seawater = 1.5 × 10^21 L × 1000 mL/L = 1.5 × 10^24 mL
Step 2: Calculate the mass of the seawater in grams
Mass = Volume × Density
Mass of seawater in grams = 1.5 × 10^24 mL × 1.03 g/mL = 1.545 × 10^24 g
Step 3: Calculate the mass of sodium chloride in grams
Mass of sodium chloride = 3.1% of mass of seawater
Mass of sodium chloride in grams = (3.1/100) × 1.545 × 10^24 g = 4.7895 × 10^22 g
Step 4: Convert the mass of sodium chloride to kilograms and tons
1 kg = 1000 g
1 ton = 2000 lb = 2000 lb × 453.6 g/lb = 907,200 g
Mass of sodium chloride in kilograms = 4.7895 × 10^22 g ÷ 1000 = 4.7895 × 10^19 kg
Mass of sodium chloride in tons = 4.7895 × 10^22 g ÷ 907,200 = 5.274 × 10^16 tons
Therefore, the total mass of sodium chloride is approximately 4.7895 × 10^19 kilograms and 5.274 × 10^16 tons.
To calculate the total mass of sodium chloride in kilograms, we first need to determine the volume of seawater in liters. We'll then use the density of seawater to convert its volume to mass, and finally, calculate the mass of sodium chloride.
Let's break down the problem step by step:
Step 1: Convert the volume of seawater to liters.
The given volume of seawater is 1.5 × 10^21 L.
Step 2: Calculate the mass of seawater using its density.
The density of seawater is given as 1.03 g/mL.
We need to convert the volume from liters to milliliters to use the density calculation properly.
Since 1 L = 1000 mL, we can multiply the volume of seawater by 1000 to convert to milliliters.
1.5 × 10^21 L × 1000 mL/L = 1.5 × 10^24 mL
To calculate the mass of seawater, we multiply the volume (in mL) by the density (in g/mL):
Mass of seawater = Volume × Density
Mass of seawater = 1.5 × 10^24 mL × 1.03 g/mL
Step 3: Calculate the mass of sodium chloride.
We are told that seawater contains 3.1% sodium chloride by mass.
To calculate the mass of sodium chloride, we need to find 3.1% of the mass of seawater.
Mass of sodium chloride = 3.1% of Mass of seawater
Step 4: Convert the mass of sodium chloride to kilograms and tons.
To convert the mass to kilograms, we divide it by 1000 (since 1 kg = 1000 g).
To convert the mass to tons, we divide it by 1000 (since 1 ton = 1000 kg).
Finally, let's calculate the mass of sodium chloride:
Mass of seawater = 1.5 × 10^24 mL × 1.03 g/mL
Mass of sodium chloride = 3.1% of Mass of seawater
Mass of sodium chloride in kilograms = Mass of sodium chloride / 1000
Mass of sodium chloride in tons = Mass of sodium chloride / 1000
Now, you can substitute the values into the equations, perform the calculations, and find the total mass of sodium chloride in kilograms and tons.
1.03 g/mL x 1000 mL x 0.031 = ? g NaCl in 1L
? g NaCl/L x 1.5E21 L = mass NaCl in total sea water.
Convert from grams to kg and tons. The conversion factors are given.