Magnesium silicate is a compound of magnesium oxide and silicon. It is the magnesium salt of silicic acid containing an unspecified amount of water. The molecular formula can be expressed more clearly as MgSiO3.
<u>Answer:</u> The time taken by the reaction is 84.5 seconds
<u>Explanation:</u>
The equation used to calculate half life for first order kinetics:

where,
= half-life of the reaction = 9.0 s
k = rate constant = ?
Putting values in above equation, we get:

Rate law expression for first order kinetics is given by the equation:
......(1)
where,
k = rate constant = 
t = time taken for decay process = 50.7 sec
= initial amount of the reactant = ?
[A] = amount left after decay process = 0.0741 M
Putting values in equation 1, we get:
![0.077=\frac{2.303}{50.7}\log\frac{[A_o]}{0.0741}](https://tex.z-dn.net/?f=0.077%3D%5Cfrac%7B2.303%7D%7B50.7%7D%5Clog%5Cfrac%7B%5BA_o%5D%7D%7B0.0741%7D)
![[A_o]=3.67M](https://tex.z-dn.net/?f=%5BA_o%5D%3D3.67M)
Now, calculating the time taken by using equation 1:
![[A]=0.0055M](https://tex.z-dn.net/?f=%5BA%5D%3D0.0055M)

![[A_o]=3.67M](https://tex.z-dn.net/?f=%5BA_o%5D%3D3.67M)
Putting values in equation 1, we get:

Hence, the time taken by the reaction is 84.5 seconds
Answer:
The granite block transferred <u>4080 joules</u> of energy, and the mass of the water is <u>35.84 grams</u>.
Explanation:
The equation needed to answer both parts of the question is:
Q = mcΔT
In this equation,
-----> Q = energy/heat (J)
-----> m = mass (g)
-----> c = specific heat (J/g°C)
-----> ΔT = change in temperature (°C)
<u>Part #1:</u>
First, you need to find the energy transferred from granite block using the previous equation. You have been given the mass, specific heat, and change in temperature.
Q = ? J c = 0.795 J/g°C
m = 126.1 g ΔT = 92.6 °C - 51.9 °C = 40.7 °C
Q = mcΔT
Q = (126.1 g)(0.795 J/g°C)(40.7 )
Q = 4080
<u>Part #2:</u>
Secondly, using the energy calculated in Part #1, you need to calculate the mass of the water. You have calculated the energy transferred, and have been given the specific heat and change in temperature.
Q = 4080 J c = 4.186 J/g°C
m = ? g ΔT = 51.9 °C - 24.7 °C = 27.2 °C
Q = mcΔT
4080 J = m(4.186 J/g°C)(27.2 °C)
4080 J = m(113.8592)
35.84 = m