Answer :
Final answer:
The mass of one cup of water with added salt is the sum of the water's mass and the salt's mass. The mass increases by 5 grams per teaspoon of salt, and therefore, the density increases slightly. To calculate the exact density, one must consider the change in volume due to the added salt.
Explanation:
Understanding Mass and Density in Solutions
The mass of one cup of water combined with a substance such as salt can be found by adding the mass of the water to the mass of the salt. The density of a solution can also be determined and is a measure of the concentration of the substance in the solution.
One cup of water is approximately 237 milliliters, and water has a density of 1 gram per milliliter, so the mass of one cup of water is approximately 237 grams. To find the total mass with salt added, you need to know that one teaspoon of salt weighs about 5 grams. Therefore:
Mass of 1 cup of water + 2 teaspoons of salt = 237 grams (water) + 2 x 5 grams (salt) = 247 grams
Mass of 1 cup of water + 3 teaspoons of salt = 237 grams (water) + 3 x 5 grams (salt) = 252 grams
Mass of 1 cup of water + 4 teaspoons of salt = 237 grams (water) + 4 x 5 grams (salt) = 257 grams
To find the density, you can use the formula Density = Mass / Volume. If the volume remains constant (1 cup), adding salt increases the mass, so the density increases as well. However, calculations for density here would require an adjustment for the volume of the salt.
Given the density of a dissolved substance is its concentration, adding salt increases the density. Using the concentration of 1M for a liter of water dissolved with 58 grams of salt as a reference, slight density changes occur with teaspoons of salt since they are less than 58 grams. Thus, the density with salt added will be slightly higher than 1 g/ml but requires precise volume change measurements to calculate.
Q1. What is the mass of 1 cup of water and 2 teaspoons of salt?
The answer is 258 g.
Density (D) is mass (m) divided by volume (V): D = m/V
So, m = D * V
According to the US units, the volume of 1 cup is: V = 236.6 cm³.
The density of the water is: D = 1 g/cm³.
So, the mass of 1 cup of water is: m = 1 g/cm³ * 236.6 cm³ = 236.6 g.
According to the US units, the volume of 1 teaspoon is: V = 4.93 cm³.
The density of salt is: D = 2.17 g/cm³.
So, the mass of 1 teaspoon of salt is: m = 2.17 g/cm³ * 4.93 cm³ = 10.7 g.
The mass of 1 cup of water and 2 teaspoons of salt is
236.6 g + 2 * 10.7 g = 236.6 g + 21.4 g = 258 g.
Q2. What is the density of 1 cup of water and 2 teaspoons of salt?
The answer is 3.17 g/cm³.
Density (D) is mass (m) divided by volume (V): D = m/V
According to the US units, the volume of 1 cup is: V = 236.6 cm³.
The mass of 1 cup of water from question 1 is: m = 236.6 g.
So, the density of 1 cup of water is: D = 236.6 g / 236.6 cm³ = 1 g/cm³
According to the US units, the volume of 1 teaspoon is 4.93 cm³. The volume of 2 teaspoons is: V = 2 * 4.93 cm³ = 9.86 cm³.
The mass of 1 teaspoon of salt from question 1 is: m = 10.7 g. The mass of 2 teaspoons of salt is: m = 2 * 10.7 g = 21.4 g.
So, the density of 2 teaspoons of salt is: D = 21.4 g / 9.86 cm³ = 2.17 g/cm³
The density of 1 cup of water and 2 teaspoons of salt is:
1 g/cm³ + 2.17 g/cm³ = 3.17 g/cm³
Q3. What is the mass of 1 cup of water and 3 teaspoons of salt?
The answer is 268.7 g.
Density (D) is mass (m) divided by volume (V): D = m/V
So, m = D * V
According to the US units, the volume of 1 cup is: V = 236.6 cm³.
The density of the water is: D = 1 g/cm³.
So, the mass of 1 cup of water is: m = 1 g/cm³ * 236.6 cm³ = 236.6 g.
According to the US units, the volume of 1 teaspoon is: V = 4.93 cm³.
The density of salt is: D = 2.17 g/cm³.
So, the mass of 1 teaspoon of salt is: m = 2.17 g/cm³ * 4.93 cm³ = 10.7 g.
The mass of 1 cup of water and 3 teaspoons of salt is
236.6 g + 3 * 10.7 g = 236.6 g + 32.1 g = 268.7 g.
Q4. What is the density of 1 cup of water and 3 teaspoons of salt?
The answer is 3.17 g/cm³
Density (D) is mass (m) divided by volume (V): D = m/V
According to the US units, the volume of 1 cup is: V = 236.6 cm³.
The mass of 1 cup of water from question 1 is: m = 236.6 g.
So, the density of 1 cup of water is: D = 236.6 g / 236.6 cm³ = 1 g/cm³
According to the US units, the volume of 1 teaspoon is 4.93 cm³. The volume of 3 teaspoons is: V = 3 * 4.93 cm³ = 14.79 cm³.
The mass of 1 teaspoon of salt from question 1 is: m = 10.7 g. The mass of 3 teaspoons of salt is: m = 3 * 10.7 g = 32.1 g.
So, the density of 3 teaspoons of salt is: D = 32.1 g / 14.79 cm³ = 2.17 g/cm³
The density of 1 cup of water and 3 teaspoons of salt is:
1 g/cm³ + 2.17 g/cm³ = 3.17 g/cm³
Q5. What is the mass of 1 cup of water and 4 teaspoons of salt?
The answer is 279.4 g.
Density (D) is mass (m) divided by volume (V): D = m/V
So, m = D * V
According to the US units, the volume of 1 cup is: V = 236.6 cm³.
The density of the water is: D = 1 g/cm³.
So, the mass of 1 cup of water is: m = 1 g/cm³ * 236.6 cm³ = 236.6 g.
According to the US units, the volume of 1 teaspoon is: V = 4.93 cm³.
The density of salt is: D = 2.17 g/cm³.
So, the mass of 1 teaspoon of salt is: m = 2.17 g/cm³ * 4.93 cm³ = 10.7 g.
The mass of 1 cup of water and 4 teaspoons of salt is
236.6 g + 4 * 10.7 g = 236.6 g + 42.8 g = 279.4 g.
Q6. What is the density of 1 cup of water and 4 teaspoons of salt?
The answer is 3.17 g/cm³
Density (D) is mass (m) divided by volume (V): D = m/V
According to the US units, the volume of 1 cup is: V = 236.6 cm³.
The mass of 1 cup of water from question 1 is: m = 236.6 g.
So, the density of 1 cup of water is: D = 236.6 g / 236.6 cm³ = 1 g/cm³
According to the US units, the volume of 1 teaspoon is 4.93 cm³. The volume of 4 teaspoons is: V = 4 * 4.93 cm³ = 19.72 cm³.
The mass of 1 teaspoon of salt from question 1 is: m = 10.7 g. The mass of 4 teaspoons of salt is: m = 4 * 10.7 g = 42.8 g.
So, the density of 3 teaspoons of salt is: D = 42.8 g / 19.72 cm³ = 2.17 g/cm³
The density of 1 cup of water and 4 teaspoons of salt is:
1 g/cm³ + 2.17 g/cm³ = 3.17 g/cm³
The answer is 258 g.
Density (D) is mass (m) divided by volume (V): D = m/V
So, m = D * V
According to the US units, the volume of 1 cup is: V = 236.6 cm³.
The density of the water is: D = 1 g/cm³.
So, the mass of 1 cup of water is: m = 1 g/cm³ * 236.6 cm³ = 236.6 g.
According to the US units, the volume of 1 teaspoon is: V = 4.93 cm³.
The density of salt is: D = 2.17 g/cm³.
So, the mass of 1 teaspoon of salt is: m = 2.17 g/cm³ * 4.93 cm³ = 10.7 g.
The mass of 1 cup of water and 2 teaspoons of salt is
236.6 g + 2 * 10.7 g = 236.6 g + 21.4 g = 258 g.
Q2. What is the density of 1 cup of water and 2 teaspoons of salt?
The answer is 3.17 g/cm³.
Density (D) is mass (m) divided by volume (V): D = m/V
According to the US units, the volume of 1 cup is: V = 236.6 cm³.
The mass of 1 cup of water from question 1 is: m = 236.6 g.
So, the density of 1 cup of water is: D = 236.6 g / 236.6 cm³ = 1 g/cm³
According to the US units, the volume of 1 teaspoon is 4.93 cm³. The volume of 2 teaspoons is: V = 2 * 4.93 cm³ = 9.86 cm³.
The mass of 1 teaspoon of salt from question 1 is: m = 10.7 g. The mass of 2 teaspoons of salt is: m = 2 * 10.7 g = 21.4 g.
So, the density of 2 teaspoons of salt is: D = 21.4 g / 9.86 cm³ = 2.17 g/cm³
The density of 1 cup of water and 2 teaspoons of salt is:
1 g/cm³ + 2.17 g/cm³ = 3.17 g/cm³
Q3. What is the mass of 1 cup of water and 3 teaspoons of salt?
The answer is 268.7 g.
Density (D) is mass (m) divided by volume (V): D = m/V
So, m = D * V
According to the US units, the volume of 1 cup is: V = 236.6 cm³.
The density of the water is: D = 1 g/cm³.
So, the mass of 1 cup of water is: m = 1 g/cm³ * 236.6 cm³ = 236.6 g.
According to the US units, the volume of 1 teaspoon is: V = 4.93 cm³.
The density of salt is: D = 2.17 g/cm³.
So, the mass of 1 teaspoon of salt is: m = 2.17 g/cm³ * 4.93 cm³ = 10.7 g.
The mass of 1 cup of water and 3 teaspoons of salt is
236.6 g + 3 * 10.7 g = 236.6 g + 32.1 g = 268.7 g.
Q4. What is the density of 1 cup of water and 3 teaspoons of salt?
The answer is 3.17 g/cm³
Density (D) is mass (m) divided by volume (V): D = m/V
According to the US units, the volume of 1 cup is: V = 236.6 cm³.
The mass of 1 cup of water from question 1 is: m = 236.6 g.
So, the density of 1 cup of water is: D = 236.6 g / 236.6 cm³ = 1 g/cm³
According to the US units, the volume of 1 teaspoon is 4.93 cm³. The volume of 3 teaspoons is: V = 3 * 4.93 cm³ = 14.79 cm³.
The mass of 1 teaspoon of salt from question 1 is: m = 10.7 g. The mass of 3 teaspoons of salt is: m = 3 * 10.7 g = 32.1 g.
So, the density of 3 teaspoons of salt is: D = 32.1 g / 14.79 cm³ = 2.17 g/cm³
The density of 1 cup of water and 3 teaspoons of salt is:
1 g/cm³ + 2.17 g/cm³ = 3.17 g/cm³
Q5. What is the mass of 1 cup of water and 4 teaspoons of salt?
The answer is 279.4 g.
Density (D) is mass (m) divided by volume (V): D = m/V
So, m = D * V
According to the US units, the volume of 1 cup is: V = 236.6 cm³.
The density of the water is: D = 1 g/cm³.
So, the mass of 1 cup of water is: m = 1 g/cm³ * 236.6 cm³ = 236.6 g.
According to the US units, the volume of 1 teaspoon is: V = 4.93 cm³.
The density of salt is: D = 2.17 g/cm³.
So, the mass of 1 teaspoon of salt is: m = 2.17 g/cm³ * 4.93 cm³ = 10.7 g.
The mass of 1 cup of water and 4 teaspoons of salt is
236.6 g + 4 * 10.7 g = 236.6 g + 42.8 g = 279.4 g.
Q6. What is the density of 1 cup of water and 4 teaspoons of salt?
The answer is 3.17 g/cm³
Density (D) is mass (m) divided by volume (V): D = m/V
According to the US units, the volume of 1 cup is: V = 236.6 cm³.
The mass of 1 cup of water from question 1 is: m = 236.6 g.
So, the density of 1 cup of water is: D = 236.6 g / 236.6 cm³ = 1 g/cm³
According to the US units, the volume of 1 teaspoon is 4.93 cm³. The volume of 4 teaspoons is: V = 4 * 4.93 cm³ = 19.72 cm³.
The mass of 1 teaspoon of salt from question 1 is: m = 10.7 g. The mass of 4 teaspoons of salt is: m = 4 * 10.7 g = 42.8 g.
So, the density of 3 teaspoons of salt is: D = 42.8 g / 19.72 cm³ = 2.17 g/cm³
The density of 1 cup of water and 4 teaspoons of salt is:
1 g/cm³ + 2.17 g/cm³ = 3.17 g/cm³
