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Sagot :
Answer: 5.1 x 10⁻¹ kg
To find the mass of water in the bottle, we can multiply the mass of one molecule by the number of molecules.
Dimensional Analysis
By using dimensional analysis, or by cancelling out units, we can figure out what to multiply or divide. Dimensional analysis uses fractions written with units. Dividing the same unit cancels out units we don't need.
To solve:
- Figure out what units we need in the answer.
- Write the fractions using given information from the question.
- Put the fractions in an equation.
- Cancel out units to solve.
Units we need in the answer
We are looking for the mass of H₂O in the bottle.
The units we need in the answer are: [tex]\displaystyle{ \frac{kg}{bottle} }[/tex]
Write fractions with given information
The question tells us:
- the mass of one H₂O molecule is 3 x 10⁻²⁹ kg: [tex]\displaystyle{ \frac{(3 * 10^{-29}\ kg)}{1\ H_{2}O}}[/tex]
- the bottle has 1.7 x 10²⁸ molecules of H₂O: [tex]\displaystyle{ \frac{(1.7*10^{28}\ H_{2}O)}{1\ bottle}}[/tex]
Write an equation
Our equation puts the fractions in an equation, making them multiply to get the units we need.
[tex]\displaystyle{ \frac{(3 * 10^{-29}\ kg)}{1\ H_{2}O} \ *\ \frac{(1.7*10^{28}\ H_{2}O)}{1\ bottle}}\ =\ \frac{kg}{bottle}[/tex]
Why is this equation correct?
Remember that dividing the same unit will cancel them out. In the equation, we have H₂O in a numerator and H₂O in a denominator. So, H₂O will cancel out. In the end, we will only have kg in the numerator and bottle in the denominator.
Cancel out units to solve
Take the equation we wrote. Now that we know our equation gives us the right units, we only need the front part.
[tex]\displaystyle{ \frac{(3 * 10^{-29}\ kg)}{1\ H_{2}O} \ *\ \frac{(1.7*10^{28}\ H_{2}O)}{1\ bottle}}[/tex]
Cancel out H₂O:
[tex]=\displaystyle{ \frac{(3 * 10^{-29}\ kg)}{1} \ *\ \frac{(1.7*10^{28})}{1\ bottle}}[/tex]
Simplify the equation:
[tex]=\displaystyle{ \frac{(3 * 10^{-29})*(1.7*10^{28})\ kg}{1\ bottle}[/tex]
[tex]=\displaystyle{ \frac{3 * 10^{-29}*1.7*10^{28}\ kg}{1\ bottle}[/tex]
Use exponent rules to multiply 10⁻²⁹ with 10²⁸:
[tex]=\displaystyle{ \frac{3 *1.7*10^{28-29}\ kg}{1\ bottle}[/tex]
[tex]=\displaystyle{ \frac{3*1.7*10^{-1}\ kg}{1\ bottle}[/tex]
Multiply within the numerator to simplify:
[tex]=\displaystyle{ \frac{5.1*10^{-1}\ kg}{1\ bottle}[/tex]
∴ The mass of water in the bottle is 5.1 x 10⁻¹ kg.
Learn more about finding the total mass of many molecules together here: https://brainly.com/question/18838161
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