a
A man pushes a canoe off the shore and into the water.
b
A car passenger moves forward when a car suddenly stops.
c
A rocket lifts off from a launch pad.
d
A shopping cart accelerates when it is pushed.
11 answers
The scenario that best demonstrates Newton's first law of motion is:
b A car passenger moves forward when a car suddenly stops.
Newton's first law states that an object at rest will remain at rest, and an object in motion will remain in motion with the same speed and in the same direction unless acted upon by an unbalanced force. In this scenario, the car is the object that is suddenly stopped (an external force is applied), but the passenger continues moving forward due to inertia.
To find out how many half-lives have occurred after 67.5 hours for a radioisotope with a half-life of 7.5 hours, you can use the formula:
\[ \text{Number of half-lives} = \frac{\text{Total time elapsed}}{\text{Half-life duration}} \]
Substituting the values:
\[ \text{Number of half-lives} = \frac{67.5 \text{ hours}}{7.5 \text{ hours}} = 9 \]
Thus, the answer is:
c: 9 half-lives.
Fiona's data does support the law of conservation of matter, which states that matter cannot be created or destroyed in a chemical reaction; thus, the mass of the reactants must equal the mass of the products.
Since Fiona found that the total mass of the reactants (55 grams) is the same as the total mass of the products (55 grams) after the reaction, the correct answer is:
b: Yes, because the mass of the reactants is the same as the mass of the products in her data.
To balance the chemical equation for the reaction between iron (Fe) and chlorine gas (Cl₂) to form iron(III) chloride (FeCl₃), we follow the law of conservation of mass, which requires that the number of atoms of each element on the reactant side (left) must equal the number of atoms on the product side (right).
The unbalanced equation is:
\[ \text{Fe} + \text{Cl}_2 \rightarrow \text{FeCl}_3 \]
On the left side, we have:
On the right side, we have:
To balance the chlorine atoms, we can use a coefficient of 3 in front of FeCl₃ and a coefficient of 3 in front of Cl₂, yielding:
\[ 2\text{Fe} + 3\text{Cl}_2 \rightarrow 2\text{FeCl}_3 \]
Now we can count:
Left side:
Right side:
Now both sides are balanced.
Thus, the coefficients in order from left to right, for Fe, Cl₂, and FeCl₃, are:
2, 3, 2
To balance the equation \( \text{N}_2 + \text{H}_2 \rightarrow \text{NH}_3 \) according to the conservation of mass, we need to first determine how many nitrogen (N) and hydrogen (H) atoms are present on both sides of the equation.
On the reactant side:
On the product side:
To balance the equation:
Putting it all together, we have the coefficients:
Therefore:
In summary:
So the matches are:
Here’s the matching of the equations in Column A to their corresponding reaction types in Column B:
Synthesis:
a. \( \text{Na} + \text{Cl} \rightarrow \text{NaCl} \)
(Synthesis reactions involve two or more reactants combining to form a single product.)
Single Replacement:
c. \( 2 \text{NaCl} + \text{Br}_2 \rightarrow 2 \text{NaBr} + \text{Cl}_2 \)
(Single replacement reactions involve one element displacing another in a compound.)
Combustion:
b. \( \text{C}_3\text{H}_8 + 5 \text{O}_2 \rightarrow 3 \text{CO}_2 + 4 \text{H}_2\text{O} \)
(Combustion reactions typically involve a hydrocarbon reacting with oxygen to produce carbon dioxide and water.)
Double Displacement:
e. \( \text{MgBr}_2 + 2 \text{NaCl} \rightarrow \text{MgCl}_2 + 2 \text{NaBr} \)
(Double displacement reactions involve the exchange of ions between two compounds.)
Decomposition:
d. \( 2 \text{H}_2\text{O} \rightarrow 2 \text{H}_2 + \text{O}_2 \)
(Decomposition reactions involve a single compound breaking down into two or more products.)
So, the final matches are:
