Saygo, Joshua Gabriel C.
2CHE-B
SAQ 1-1
Show the derivation of the following units, in terms of the seven base SI units:
(a) Newtons (N)
𝐹 = 𝑚𝑔
𝐹 =𝑚𝑥
𝑣
𝑡
𝑚
𝐹 = 𝑘𝑔 𝑥 𝑠 ; 𝑭 = 𝒌𝒈 ∗ 𝒎/𝒔𝟐
𝑠
(b) Joules (J)
𝐽𝑜𝑢𝑙𝑒 𝑖𝑠 𝑎 𝑢𝑛𝑖𝑡 𝑜𝑓 𝑤𝑜𝑟𝑘; 𝑤𝑜𝑟𝑘 = 𝑓𝑜𝑟𝑐𝑒 𝑥 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡
𝑤𝑜𝑟𝑘 = 𝑚𝑔 𝑥 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡
𝑚
𝑤𝑜𝑟𝑘 = 𝑘𝑔 𝑥 𝑠 𝑥 𝑚
𝑠
𝑱 = 𝒌𝒈 ∗ 𝒎𝟐 /𝒔𝟐
(c) Watts (W)
𝑊𝑎𝑡𝑡 𝑖𝑠 𝑎 𝑢𝑛𝑖𝑡 𝑜𝑓 𝑝𝑜𝑤𝑒𝑟; 𝑝𝑜𝑤𝑒𝑟 =
𝑘𝑔 ∗
𝑝𝑜𝑤𝑒𝑟 =
𝑤𝑜𝑟𝑘
𝑡𝑖𝑚𝑒
𝑚2
𝑠2
𝑠
𝑾 = 𝒌𝒈 ∗ 𝒎𝟐 /𝒔𝟑
(d) Pascals (Pa)
𝑃𝑎𝑠𝑐𝑎𝑙 𝑖𝑠 𝑎 𝑢𝑛𝑖𝑡 𝑜𝑓 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒; 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 =
𝑘𝑔 ∗
𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 =
𝑷𝒂 =
𝑚
𝑠2
𝑚2
𝒌𝒈
𝒎 ∗ 𝒔𝟐
𝑓𝑜𝑟𝑐𝑒
𝑎𝑟𝑒𝑎
Saygo, Joshua Gabriel C.
2CHE-B
(e) Volts (V)
𝑚2
(𝑘𝑔 ∗ 3 )
𝑤𝑜𝑟𝑘
𝑠
𝑉𝑜𝑙𝑡𝑎𝑔𝑒 =
; 𝑉𝑜𝑙𝑡𝑎𝑔𝑒 =
𝑎𝑚𝑝𝑒𝑟𝑒
𝐴
𝑽=
𝒌𝒈 ∗ 𝒎𝟐
𝒔𝟑 ∗ 𝑨
SAQ 1-2
Show the equivalence of the units on either side of the following equations:
(a) 𝑃𝑉 = 𝑛𝑅𝑇 (pressure × volume = number of moles × ideal gas constant × temperature)
(𝑎𝑡𝑚)(𝐿) = ( 𝑚𝑜𝑙) (0.082
𝐿 ∗ 𝑎𝑡𝑚
) (𝐾)
𝐾 ∗ 𝑚𝑜𝑙
(b) 𝛥𝐺 = 𝛥𝐻 − 𝑇𝛥𝑆 (change in molar Gibbs energy = change in molar enthalpy – temperature ×
change in molar entropy)
(
𝑘𝐽
𝑘𝐽
𝑘𝐽
)=(
) − (𝐾) (
)
(𝐾)(𝑚𝑜𝑙)
𝑚𝑜𝑙
𝑚𝑜𝑙
(c) 𝛥𝑝 = ℎ𝜌𝑔 (pressure difference = height × fluid density × acceleration due to gravity)
(𝑃𝑎) = (𝑚) (
𝑘𝑔 𝑚
)( )
𝑚3 𝑠 2
SAQ 1-3
Use the equivalence of units on either side of an equation to determine the missing symbol in the
following equation for the measurement of the surface tension of a fluid via the capillary rise method:
𝛾 = 𝑟𝑔 ? ℎ 2𝑐𝑜𝑠𝜃
(where  = surface tension of the fluid, r = radius of the capillary, g = acceleration due to gravity, ? = to
be determined, h = height of the liquid rise,  = contact angle)
𝑁
𝐹 (𝑚)
𝛾 = 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑡𝑒𝑛𝑠𝑖𝑜𝑛 =
𝐿 (𝑚)
Saygo, Joshua Gabriel C.
2CHE-B
𝑚
𝑠 2 = 𝑟𝑔(𝑋)ℎ
𝑚
2 cos 𝜃
𝑚
𝑚
𝑘𝑔 ∗ 2 (𝑚) ( 2 ) (𝑋)(𝑚)
𝑠 =
𝑠
𝑚
2 cos 𝜃
𝑚
𝑘𝑔 ∗ 2
𝑠 = (( 𝑚 )(𝑋))/(𝑚)
𝑚
𝑠2
𝑘𝑔 ∗
𝑿 = 𝒌𝒈
SAQ 1-4
Calculate the height of a column of water equivalent to 1.00 bar
1.00 𝑏𝑎𝑟 = 1 𝑥 105 𝑃𝑎 = 1 𝑥 105 𝑁/𝑚2
𝑃 = 𝜌𝑔ℎ
1 𝑥 10
5
𝑚
𝑠 2 = 997 𝑘𝑔 𝑥 9.81 𝑚 𝑥 (ℎ)
𝑚2
𝑚3
𝑠2
𝑘𝑔 ∗
(
1 𝑥 105 𝑘𝑔 ∗
ℎ=
(997
𝑚2
𝑚
𝑠2 )
𝑘𝑔
𝑚
) (9.81 2 )
𝑚3
𝑠
𝑚
1
1 𝑚3
1 𝑠2
ℎ = (1 𝑥 10 𝑘𝑔 ∗ 2 ) ( 2 ) (
)(
)
𝑠
𝑚
997 𝑘𝑔 9.81 𝑚
5
𝒉 = 𝟏𝟎. 𝟐𝟐𝟒 𝒎