Answer:
10 g
Explanation:
Right from the start, just by inspecting the values given, you can say that the answer will be
10 g
.
Now, here's what that is the case.
As you know, a substance's specific heat tells you how much heat is needed to increase the temperature of
1 g
of that substance by
1
∘
C
.
Water has a specific heat of approximately
4.18
J
g
∘
C
. This tells you that in order to increase the temperature of
1 g
of water by
1
∘
C
, you need to provide
4.18 J
of heat.
Now, how much heat would be required to increase the temperature of
1 g
of water by
10
∘
C
?
Well, you'd need
4.18 J
to increase it by
1
∘
C
, another
4.18 J
to increase it by another
1
∘
C
, and so on. This means that you'd need
4.18 J
×
10
=
41.8 J
to increase the temperature of
1 g
of water by
10
∘
C
.
Now look at the value given to you. If you need
41.8 J
to increase the temperature of
1 g
of water by
10
∘
C
, what mass of water would require
10
times as much heat to increase its temperature by
10
∘
C
?
1 g
×
10
=
10 g
And that's your answer.
Mathematically, you can calculate this by using the equation
q
=
m
⋅
c
⋅
Δ
T
, where
q
- heat absorbed/lost
m
- the mass of the sample
c
- the specific heat of the substance
Δ
T
- the change in temperature, defined as final temperature minus initial temperature
Plug in your values to get
418
J
=
m
⋅
4.18
J
g
∘
C
⋅
(
20
−
10
)
∘
C
m
=
418
4.18
⋅
10
=
10 g
= 1.67 mol NaN₃